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Dr. Shaobo He
Central south university

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Research Keywords & Expertise

0 Nonlinear
0 Fractional Calculus and Applications
0 Fractional differential equations
0 chaotic communications and security
0 Chaos theory and its application

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Nonlinear
Fractional Calculus and Applications
Fractional differential equations
nonlinear circuits

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Research article
Published: 01 August 2021 in Chaos: An Interdisciplinary Journal of Nonlinear Science
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We propose herein a novel discrete hyperchaotic map based on the mathematical model of a cycloid, which produces multistability and infinite equilibrium points. Numerical analysis is carried out by means of attractors, bifurcation diagrams, Lyapunov exponents, and spectral entropy complexity. Experimental results show that this cycloid map has rich dynamical characteristics including hyperchaos, various bifurcation types, and high complexity. Furthermore, the attractor topology of this map is extremely sensitive to the parameters of the map. The x--y plane of the attractor produces diverse shapes with the variation of parameters, and both the x--z and y--z planes produce a full map with good ergodicity. Moreover, the cycloid map has good resistance to parameter estimation, and digital signal processing implementation confirms its feasibility in digital circuits, indicating that the cycloid map may be used in potential applications.

ACS Style

Chunyi Dong; Kehui Sun; Shaobo He; Huihai Wang. A hyperchaotic cycloid map with attractor topology sensitive to system parameters. Chaos: An Interdisciplinary Journal of Nonlinear Science 2021, 31, 083132 .

AMA Style

Chunyi Dong, Kehui Sun, Shaobo He, Huihai Wang. A hyperchaotic cycloid map with attractor topology sensitive to system parameters. Chaos: An Interdisciplinary Journal of Nonlinear Science. 2021; 31 (8):083132.

Chicago/Turabian Style

Chunyi Dong; Kehui Sun; Shaobo He; Huihai Wang. 2021. "A hyperchaotic cycloid map with attractor topology sensitive to system parameters." Chaos: An Interdisciplinary Journal of Nonlinear Science 31, no. 8: 083132.

Preprint content
Published: 26 July 2021
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Since the concept of discrete memristor was proposed, more and more scholars began to study this topic. At present, most of the works on the discrete memristor are devoted to the mathematical modeling and circuit implementation, but the research on its synchronization control has not received much attention. This paper focuses on the parameter identification for the discrete memristive chaotic map, and a modified intelligent optimization algorithm named adaptive differential evolution algorithm is proposed. To deal with the complex behaviors of hyperchaos and coexisting attractors of the considered discrete memristive chaotic maps, the identification objective function adopts two special parts: time sequences and return maps. Numerical simulations demonstrate that the proposed algorithm has the best performance among the six existing algorithms, and it can still accurately identify the parameters of the original system under noise interference.

ACS Style

Yuexi Peng; Shaobo He; Kehui Sun. Parameter Identification for Discrete Memristive Chaotic Map using Adaptive Differential Evolution Algorithm. 2021, 1 .

AMA Style

Yuexi Peng, Shaobo He, Kehui Sun. Parameter Identification for Discrete Memristive Chaotic Map using Adaptive Differential Evolution Algorithm. . 2021; ():1.

Chicago/Turabian Style

Yuexi Peng; Shaobo He; Kehui Sun. 2021. "Parameter Identification for Discrete Memristive Chaotic Map using Adaptive Differential Evolution Algorithm." , no. : 1.

Journal article
Published: 22 July 2021 in Entropy
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Properly measuring the complexity of time series is an important issue. The permutation entropy (PE) is a widely used as an effective complexity measurement algorithm, but it is not suitable for the complexity description of multi-dimensional data. In this paper, in order to better measure the complexity of multi-dimensional time series, we proposed a modified multivariable PE (MMPE) algorithm with principal component analysis (PCA) dimensionality reduction, which is a new multi-dimensional time series complexity measurement algorithm. The analysis results of different chaotic systems verify that MMPE is effective. Moreover, we applied it to the comlexity analysis of EEG data. It shows that the person during mental arithmetic task has higher complexity comparing with the state before mental arithmetic task. In addition, we also discussed the necessity of the PCA dimensionality reduction.

ACS Style

Dizhen Ma; Shaobo He; Kehui Sun. A Modified Multivariable Complexity Measure Algorithm and Its Application for Identifying Mental Arithmetic Task. Entropy 2021, 23, 931 .

AMA Style

Dizhen Ma, Shaobo He, Kehui Sun. A Modified Multivariable Complexity Measure Algorithm and Its Application for Identifying Mental Arithmetic Task. Entropy. 2021; 23 (8):931.

Chicago/Turabian Style

Dizhen Ma; Shaobo He; Kehui Sun. 2021. "A Modified Multivariable Complexity Measure Algorithm and Its Application for Identifying Mental Arithmetic Task." Entropy 23, no. 8: 931.

Journal article
Published: 20 May 2021 in Chaos: An Interdisciplinary Journal of Nonlinear Science
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Network performance of neurons plays a vital role in determining the behavior of many physiological systems. In this paper, we discuss the wave propagation phenomenon in a network of neurons considering obstacles in the network. Numerous studies have shown the disastrous effects caused by the heterogeneity induced by the obstacles, but these studies have been mainly discussing the orientation effects. Hence, we are interested in investigating the effects of both the size and orientation of the obstacles in the wave re-entry and spiral wave formation in the network. For this analysis, we have considered two types of neuron models and a pancreatic beta cell model. In the first neuron model, we use the well-known differential equation-based neuron models, and in the second type, we used the hybrid neuron models with the resetting phenomenon. We have shown that the size of the obstacle decides the spiral wave formation in the network and horizontally placed obstacles will have a lesser impact on the wave re-entry than the vertically placed obstacles.

ACS Style

Karthikeyan Rajagopal; Shaobo He; Anitha Karthikeyan; Prakash Duraisamy. Size matters: Effects of the size of heterogeneity on the wave re-entry and spiral wave formation in an excitable media. Chaos: An Interdisciplinary Journal of Nonlinear Science 2021, 31, 053131 .

AMA Style

Karthikeyan Rajagopal, Shaobo He, Anitha Karthikeyan, Prakash Duraisamy. Size matters: Effects of the size of heterogeneity on the wave re-entry and spiral wave formation in an excitable media. Chaos: An Interdisciplinary Journal of Nonlinear Science. 2021; 31 (5):053131.

Chicago/Turabian Style

Karthikeyan Rajagopal; Shaobo He; Anitha Karthikeyan; Prakash Duraisamy. 2021. "Size matters: Effects of the size of heterogeneity on the wave re-entry and spiral wave formation in an excitable media." Chaos: An Interdisciplinary Journal of Nonlinear Science 31, no. 5: 053131.

Journal article
Published: 01 April 2021 in Electronics
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In this paper, a fractional-order memristive model with infinite coexisting attractors is investigated. The numerical solution of the system is derived based on the Adomian decomposition method (ADM), and its dynamic behaviors are analyzed by means of phase diagrams, bifurcation diagrams, Lyapunov exponent spectrum (LEs), dynamic map based on SE complexity and maximum Lyapunov exponent (MLE). Simulation results show that it has rich dynamic characteristics, including asymmetric coexisting attractors with different structures and offset boosting. Finally, the digital signal processor (DSP) implementation verifies the correctness of the solution algorithm and the physical feasibility of the system.

ACS Style

Chuan Qin; Kehui Sun; Shaobo He. Characteristic Analysis of Fractional-Order Memristor-Based Hypogenetic Jerk System and Its DSP Implementation. Electronics 2021, 10, 841 .

AMA Style

Chuan Qin, Kehui Sun, Shaobo He. Characteristic Analysis of Fractional-Order Memristor-Based Hypogenetic Jerk System and Its DSP Implementation. Electronics. 2021; 10 (7):841.

Chicago/Turabian Style

Chuan Qin; Kehui Sun; Shaobo He. 2021. "Characteristic Analysis of Fractional-Order Memristor-Based Hypogenetic Jerk System and Its DSP Implementation." Electronics 10, no. 7: 841.

Journal article
Published: 24 March 2021 in Results in Physics
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The mathematical modeling of memristor in discrete-time domain is an attractive new issue, but there are still some problems to be explored. This paper studies an interesting second-order memristor-based map model, and the model is constructed to three systems based on Caputo fractional-order difference. Their dynamic behaviors are investigated by the volt–ampere curve, bifurcation diagram, maximum Lyapunov exponent, attractor phase diagram, complexity analysis and basin of attraction. Numerical simulation analysis shows that the fractional-order system exhibits quasi periodic, chaos, coexisting attractors and other complex behaviors, which demonstrates more abundant dynamic behaviors of the fractional-order form. It lays a good foundation for the future analysis or engineering application of the discrete memristor.

ACS Style

Yuexi Peng; Shaobo He; Kehui Sun. Chaos in the discrete memristor-based system with fractional-order difference. Results in Physics 2021, 24, 104106 .

AMA Style

Yuexi Peng, Shaobo He, Kehui Sun. Chaos in the discrete memristor-based system with fractional-order difference. Results in Physics. 2021; 24 ():104106.

Chicago/Turabian Style

Yuexi Peng; Shaobo He; Kehui Sun. 2021. "Chaos in the discrete memristor-based system with fractional-order difference." Results in Physics 24, no. : 104106.

Research article
Published: 18 March 2021 in Mathematical Problems in Engineering
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Chaos and control analysis for the fractional-order nonlinear circuits is a recent hot topic. In this study, a fractional-order model is deduced from a Buck-Boost converter, and its discrete solution is obtained based on the Adomian decomposition method (ADM). Chaotic dynamic characteristics of the fractional-order system are investigated by the bifurcation diagram, 0-1 test, spectral entropy (SE) algorithm, and NIST test. Meanwhile, the control of the fractional-order Buck-Boost model is discussed through two different ways, namely, the intensity feedback and the hard limiter control. Specifically, the hard limiter control can be realized using a current limiter in the circuit, where the current limiter device is applied to control the branch current. The results show that the proposed fractional-order system has complex dynamic behaviors and potential application values in the engineering field.

ACS Style

Bo Yan; Shaojie Wang; Shaobo He. Complex Dynamics and Hard Limiter Control of a Fractional-Order Buck-Boost System. Mathematical Problems in Engineering 2021, 2021, 1 -16.

AMA Style

Bo Yan, Shaojie Wang, Shaobo He. Complex Dynamics and Hard Limiter Control of a Fractional-Order Buck-Boost System. Mathematical Problems in Engineering. 2021; 2021 ():1-16.

Chicago/Turabian Style

Bo Yan; Shaojie Wang; Shaobo He. 2021. "Complex Dynamics and Hard Limiter Control of a Fractional-Order Buck-Boost System." Mathematical Problems in Engineering 2021, no. : 1-16.

Journal article
Published: 20 February 2021 in Symmetry
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By applying the Adams-Bashforth-Moulton method (ABM), this paper explores the complexity and synchronization of a fractional-order laser dynamical model. The dynamics under the variance of derivative order q and parameters of the system have examined using the multiscale complexity algorithm and the bifurcation diagram. Numerical simulation outcomes demonstrate that the system generates chaos with the decreasing of q. Moreover, this paper designs the coupled fractional-order network of laser systems and subsequently obtains its numerical solution using ABM. These solutions have demonstrated chimera states of the proposed fractional-order laser network.

ACS Style

Shaobo He; Hayder Natiq; Santo Banerjee; Kehui Sun. Complexity and Chimera States in a Network of Fractional-Order Laser Systems. Symmetry 2021, 13, 341 .

AMA Style

Shaobo He, Hayder Natiq, Santo Banerjee, Kehui Sun. Complexity and Chimera States in a Network of Fractional-Order Laser Systems. Symmetry. 2021; 13 (2):341.

Chicago/Turabian Style

Shaobo He; Hayder Natiq; Santo Banerjee; Kehui Sun. 2021. "Complexity and Chimera States in a Network of Fractional-Order Laser Systems." Symmetry 13, no. 2: 341.

Journal article
Published: 19 January 2021 in Electronics
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In order to improve the recognition rate of the biometric identification system, the features of each unimodal biometric are often combined in a certain way. However, there are some mutually exclusive redundant features in those combined features, which will degrade the identification performance. To solve this problem, this paper proposes a novel multimodal biometric identification system for face-iris recognition.It is based on binary particle swarm optimization. The face features are extracted by 2D Log-Gabor and Curvelet transform, while iris features are extracted by Curvelet transform. In order to reduce the complexity of the feature-level fusion, we propose a modified chaotic binary particle swarm optimization (MCBPSO) algorithm to select features. It uses kernel extreme learning machine (KELM) as a fitness function and chaotic binary sequences to initialize particle swarms. After the global optimal position (Gbest) is generated in each iteration, the position of Gbest is varied by using chaotic binary sequences, which is useful to realize chaotic local search and avoid falling into the local optimal position. The experiments are conducted on CASIA multimodal iris and face dataset from Chinese Academy of Sciences.The experimental results demonstrate that the proposed system can not only reduce the number of features to one tenth of its original size, but also improve the recognition rate up to 99.78%. Compared with the unimodal iris and face system, the recognition rate of the proposed system are improved by 11.56% and 2% respectively. The experimental results reveal its performance in the verification mode compared with the existing state-of-the-art systems. The proposed system is satisfactory in addressing face-iris multimodal biometric identification.

ACS Style

Qi Xiong; Xinman Zhang; Xuebin Xu; Shaobo He. A Modified Chaotic Binary Particle Swarm Optimization Scheme and Its Application in Face-Iris Multimodal Biometric Identification. Electronics 2021, 10, 217 .

AMA Style

Qi Xiong, Xinman Zhang, Xuebin Xu, Shaobo He. A Modified Chaotic Binary Particle Swarm Optimization Scheme and Its Application in Face-Iris Multimodal Biometric Identification. Electronics. 2021; 10 (2):217.

Chicago/Turabian Style

Qi Xiong; Xinman Zhang; Xuebin Xu; Shaobo He. 2021. "A Modified Chaotic Binary Particle Swarm Optimization Scheme and Its Application in Face-Iris Multimodal Biometric Identification." Electronics 10, no. 2: 217.

Research article
Published: 12 December 2020 in Complexity
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In this paper, a 4D fractional-order centrifugal flywheel governor system is proposed. Dynamics including the multistability of the system with the variation of system parameters and the derivative order are investigated by Lyapunov exponents (LEs), bifurcation diagram, phase portrait, entropy measure, and basins of attraction, numerically. It shows that the minimum order for chaos of the fractional-order centrifugal flywheel governor system is q = 0.97, and the system has rich dynamics and produces multiple coexisting attractors. Moreover, the system is controlled by introducing the adaptive controller which is proved by the Lyapunov stability theory. Numerical analysis results verify the effectiveness of the proposed method.

ACS Style

Bo Yan; Shaobo He; Shaojie Wang. Multistability in a Fractional-Order Centrifugal Flywheel Governor System and Its Adaptive Control. Complexity 2020, 2020, 1 -11.

AMA Style

Bo Yan, Shaobo He, Shaojie Wang. Multistability in a Fractional-Order Centrifugal Flywheel Governor System and Its Adaptive Control. Complexity. 2020; 2020 ():1-11.

Chicago/Turabian Style

Bo Yan; Shaobo He; Shaojie Wang. 2020. "Multistability in a Fractional-Order Centrifugal Flywheel Governor System and Its Adaptive Control." Complexity 2020, no. : 1-11.

Journal article
Published: 21 November 2020 in AEU - International Journal of Electronics and Communications
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Although memristor has been widely discussed in recent years, the topic of memristor in discrete domain is rarely mentioned. This paper presents a higher dimensional chaotic map based on the discrete memristor, and the dynamic behavior of memristor at different positions is investigated by chaotic attractor phase diagram, bifurcation diagram, system state analysis and complexity algorithm. Numerical simulations show that the discrete memristor model can not only enlarge the hyperchaotic region of the original system, but also enhance the system complexity. Furthermore, the change of memristor position in the system leads to different performance. These deserve further study and lay the foundation for the future applications of the discrete memristor.

ACS Style

Yuexi Peng; Shaobo He; Kehui Sun. A higher dimensional chaotic map with discrete memristor. AEU - International Journal of Electronics and Communications 2020, 129, 153539 .

AMA Style

Yuexi Peng, Shaobo He, Kehui Sun. A higher dimensional chaotic map with discrete memristor. AEU - International Journal of Electronics and Communications. 2020; 129 ():153539.

Chicago/Turabian Style

Yuexi Peng; Shaobo He; Kehui Sun. 2020. "A higher dimensional chaotic map with discrete memristor." AEU - International Journal of Electronics and Communications 129, no. : 153539.

Original research article
Published: 07 August 2020 in Frontiers in Applied Mathematics and Statistics
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At present, dynamics and coupled control of fractional-order non-linear systems are arousing much interest from researchers. In this paper, the fractional-order derivative is introduced into an improved memristor neural system. The dynamics of the fractional-order memristor neural model are investigated by means of bifurcation diagrams, Lyapunov exponents, and phase diagrams. To discuss the dynamical behavior of a fractional-order memristor neuron in a network, we construct a ring network of neurons and capture the spatiotemporal patterns of the neurons in the network in the presence of different excitations. Finally, the chimera state is observed, and the complexity of the network is analyzed. The analysis shows that the complexity algorithm provides a new approach for the dynamical analysis of the network.

ACS Style

Shaobo He. Complexity and Chimera States in a Ring-Coupled Fractional-Order Memristor Neural Network. Frontiers in Applied Mathematics and Statistics 2020, 6, 1 .

AMA Style

Shaobo He. Complexity and Chimera States in a Ring-Coupled Fractional-Order Memristor Neural Network. Frontiers in Applied Mathematics and Statistics. 2020; 6 ():1.

Chicago/Turabian Style

Shaobo He. 2020. "Complexity and Chimera States in a Ring-Coupled Fractional-Order Memristor Neural Network." Frontiers in Applied Mathematics and Statistics 6, no. : 1.

Original paper
Published: 13 July 2020 in Nonlinear Dynamics
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Models of neurons play an essential role in computational neuroscience. They provide a virtual laboratory to analyze the different regimes in the electrical activities of a single neuron or a network of neurons. They help the neuroscientist to have a better look at the nervous system. Some researchers have claimed that the transition of the ions through the membrane may induce an electrical field. In this paper, a new neuronal model is investigated which considers the effect of the electrical field. The dynamical properties of this model are studied. Different dynamical analyses are carried out to this end: investigating the stability of the equilibria, observing state space and trajectories, obtaining bifurcation diagram and Lyapunov exponents’ diagram, and finally exploring the basin of attraction.

ACS Style

Bo Yan; Shirin Panahi; Shaobo He; Sajad Jafari. Further dynamical analysis of modified Fitzhugh–Nagumo model under the electric field. Nonlinear Dynamics 2020, 101, 521 -529.

AMA Style

Bo Yan, Shirin Panahi, Shaobo He, Sajad Jafari. Further dynamical analysis of modified Fitzhugh–Nagumo model under the electric field. Nonlinear Dynamics. 2020; 101 (1):521-529.

Chicago/Turabian Style

Bo Yan; Shirin Panahi; Shaobo He; Sajad Jafari. 2020. "Further dynamical analysis of modified Fitzhugh–Nagumo model under the electric field." Nonlinear Dynamics 101, no. 1: 521-529.

Research article
Published: 29 June 2020 in Mathematical Problems in Engineering
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Multistablity analysis and formation of spiral wave in the fractional-order nonlinear systems is a recent hot topic. In this paper, dynamics, coexisting attractors, complexity, and synchronization of the fractional-order memristor-based hyperchaotic Lü system are investigated numerically by means of bifurcation diagram, Lyapunov exponents (LEs), chaos diagram, and sample entropy (SampEn) algorithm. The results show that the system has rich dynamics and high complexity. Meanwhile, coexisting attractors in the system are observed and hidden dynamics are illustrated by changing the initial conditions. Finally, the network based on the system is built, and the emergence of spiral waves is investigated and chimera states are observed.

ACS Style

Bo Yan; Shaobo He; Shaojie Wang. Multistability and Formation of Spiral Waves in a Fractional-Order Memristor-Based Hyperchaotic Lü System with No Equilibrium Points. Mathematical Problems in Engineering 2020, 2020, 1 -12.

AMA Style

Bo Yan, Shaobo He, Shaojie Wang. Multistability and Formation of Spiral Waves in a Fractional-Order Memristor-Based Hyperchaotic Lü System with No Equilibrium Points. Mathematical Problems in Engineering. 2020; 2020 ():1-12.

Chicago/Turabian Style

Bo Yan; Shaobo He; Shaojie Wang. 2020. "Multistability and Formation of Spiral Waves in a Fractional-Order Memristor-Based Hyperchaotic Lü System with No Equilibrium Points." Mathematical Problems in Engineering 2020, no. : 1-12.

Short communication
Published: 19 May 2020 in Chaos, Solitons & Fractals
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The realization of real memristor makes it be a very popular topic in recent years. However, the topic about discrete memristor model is rarely discussed. In this paper, a discrete memristor model is proposed based on the difference theory, and the three fingerprints characteristics are proved for this model according to the definition of the generalized memristor. This discrete model is applied to Hénon map, and we designed a new chaotic map called the discrete memristor-based Hénon map. Its dynamical behaviors are analyzed by attractor phase diagram, bifurcation diagram, Lyapunov exponent spectrum, and spectral entropy complexity algorithm. Simulation results show the performance of Hénon map is improved by applying the discrete memristor.

ACS Style

Yuexi Peng; Kehui Sun; Shaobo He. A discrete memristor model and its application in Hénon map. Chaos, Solitons & Fractals 2020, 137, 109873 .

AMA Style

Yuexi Peng, Kehui Sun, Shaobo He. A discrete memristor model and its application in Hénon map. Chaos, Solitons & Fractals. 2020; 137 ():109873.

Chicago/Turabian Style

Yuexi Peng; Kehui Sun; Shaobo He. 2020. "A discrete memristor model and its application in Hénon map." Chaos, Solitons & Fractals 137, no. : 109873.

Journal article
Published: 15 April 2020 in Chaos, Solitons & Fractals
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In the present article, as a new approach, a fuzzy disturbance observer is combined with an active controller for the synchronization of fractional-order time-delayed systems. Since the type-2 fuzzy logic system shows better performances than the type-1 fuzzy logic system on handling the uncertainties and disturbances, the type-2 fuzzy disturbance observer is utilized in this study. The stability of the proposed method is performed using the Lyapunov stability theorem and active control concept. Then, a fractional-order time-delayed financial system has been investigated, and some features of this chaotic system have been studied. Finally, by applying the proposed control scheme, synchronization results of the fractional-order time-delayed financial system when there exist time-varying disturbances are presented. Numerical simulations demonstrate the robustness and effectiveness of the proposed control technique.

ACS Style

Shaojie Wang; Stelios Bekiros; Amin Yousefpour; Shaobo He; Oscar Castillo; Hadi Jahanshahi. Synchronization of fractional time-delayed financial system using a novel type-2 fuzzy active control method. Chaos, Solitons & Fractals 2020, 136, 109768 .

AMA Style

Shaojie Wang, Stelios Bekiros, Amin Yousefpour, Shaobo He, Oscar Castillo, Hadi Jahanshahi. Synchronization of fractional time-delayed financial system using a novel type-2 fuzzy active control method. Chaos, Solitons & Fractals. 2020; 136 ():109768.

Chicago/Turabian Style

Shaojie Wang; Stelios Bekiros; Amin Yousefpour; Shaobo He; Oscar Castillo; Hadi Jahanshahi. 2020. "Synchronization of fractional time-delayed financial system using a novel type-2 fuzzy active control method." Chaos, Solitons & Fractals 136, no. : 109768.

Journal article
Published: 05 April 2020 in Symmetry
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In the present work, a new nonequilibrium four-dimensional chaotic jerk system is presented. The proposed system includes only one constant term and has coexisting and hidden attractors. Firstly, the dynamical behavior of the system is investigated using bifurcation diagrams and Lyapunov exponents. It is illustrated that this system either possesses symmetric equilibrium points or does not possess an equilibrium. Rich dynamics are found by varying system parameters. It is shown that the system enters chaos through experiencing a cascade of period doublings, and the existence of chaos is verified. Then, coexisting and hidden chaotic attractors are observed, and basin attraction is plotted. Moreover, using the multiscale C0 algorithm, the complexity of the system is investigated, and a broad area of high complexity is displayed in the parameter planes. In addition, the chaotic behavior of the system is studied by field-programmable gate array implementation. A novel methodology to discretize, simulate, and implement the proposed system is presented, and the successful implementation of the proposed system on FPGA is verified through the simulation outcome. Finally, a robust sliding mode controller is designed to suppress the chaotic behavior of the system. To deal with unexpected disturbances and uncertainties, a disturbance observer is developed along with the designed controller. To show the successful performance of the designed control scheme, numerical simulations are also presented.

ACS Style

Heng Chen; Shaobo He; Ana Dalia Pano Azucena; Amin Yousefpour; Hadi Jahanshahi; Miguel A. López; Raúl Alcaraz. A Multistable Chaotic Jerk System with Coexisting and Hidden Attractors: Dynamical and Complexity Analysis, FPGA-Based Realization, and Chaos Stabilization Using a Robust Controller. Symmetry 2020, 12, 569 .

AMA Style

Heng Chen, Shaobo He, Ana Dalia Pano Azucena, Amin Yousefpour, Hadi Jahanshahi, Miguel A. López, Raúl Alcaraz. A Multistable Chaotic Jerk System with Coexisting and Hidden Attractors: Dynamical and Complexity Analysis, FPGA-Based Realization, and Chaos Stabilization Using a Robust Controller. Symmetry. 2020; 12 (4):569.

Chicago/Turabian Style

Heng Chen; Shaobo He; Ana Dalia Pano Azucena; Amin Yousefpour; Hadi Jahanshahi; Miguel A. López; Raúl Alcaraz. 2020. "A Multistable Chaotic Jerk System with Coexisting and Hidden Attractors: Dynamical and Complexity Analysis, FPGA-Based Realization, and Chaos Stabilization Using a Robust Controller." Symmetry 12, no. 4: 569.

Accepted manuscript
Published: 27 March 2020 in Physica Scripta
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ACS Style

Yan Xiao; Kehui Sun; Shaobo He. Dynamics of a hyperchaotic map with spherical attractor. Physica Scripta 2020, 95, 065215 .

AMA Style

Yan Xiao, Kehui Sun, Shaobo He. Dynamics of a hyperchaotic map with spherical attractor. Physica Scripta. 2020; 95 (6):065215.

Chicago/Turabian Style

Yan Xiao; Kehui Sun; Shaobo He. 2020. "Dynamics of a hyperchaotic map with spherical attractor." Physica Scripta 95, no. 6: 065215.

Regular article
Published: 26 March 2020 in The European Physical Journal Special Topics
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Analyzing the chaos and bursting phenomenon of neurons has been of interest in the past decade. In this paper, we discuss an extended Hindmarsh-Rose neuron model by taking into consideration the slowly interacting cell phenomenon due to the calcium ions. In the extended model, we consider the effect of an external forcing current, and the electromagnetic coupling between the magnetic flux and the membrane potential of the neuron. We analyze the modified neuron model in the presence of periodic and quasi-periodic excitations. A more complex chaotic behavior (hyperchaos) is identified in the neuron model. The results also demonstrate the multistable nature, which was not explored earlier. To discuss the dynamical behavior of the modified neuron in a network, we construct a ring network of neurons and capture the spatiotemporal patterns of the neuron in the network, in the presence of different excitations.

ACS Style

Shaojie Wang; Shaobo He; Karthikeyan Rajagopal; Anitha Karthikeyan; Kehui Sun. Route to hyperchaos and chimera states in a network of modified Hindmarsh-Rose neuron model with electromagnetic flux and external excitation. The European Physical Journal Special Topics 2020, 229, 929 -942.

AMA Style

Shaojie Wang, Shaobo He, Karthikeyan Rajagopal, Anitha Karthikeyan, Kehui Sun. Route to hyperchaos and chimera states in a network of modified Hindmarsh-Rose neuron model with electromagnetic flux and external excitation. The European Physical Journal Special Topics. 2020; 229 (6):929-942.

Chicago/Turabian Style

Shaojie Wang; Shaobo He; Karthikeyan Rajagopal; Anitha Karthikeyan; Kehui Sun. 2020. "Route to hyperchaos and chimera states in a network of modified Hindmarsh-Rose neuron model with electromagnetic flux and external excitation." The European Physical Journal Special Topics 229, no. 6: 929-942.

Journal article
Published: 27 February 2020 in Entropy
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In this paper, dynamical behavior and synchronization of a non-equilibrium four-dimensional chaotic system are studied. The system only includes one constant term and has hidden attractors. Some dynamical features of the governing system, such as invariance and symmetry, the existence of attractors and dissipativity, chaotic flow with a plane of equilibria, and offset boosting of the chaotic attractor, are stated and discussed and a new disturbance-observer-based adaptive terminal sliding mode control (ATSMC) method with input saturation is proposed for the control and synchronization of the chaotic system. To deal with unexpected noises, an extended Kalman filter (EKF) is implemented along with the designed controller. Through the concept of Lyapunov stability, the proposed control technique guarantees the finite time convergence of the uncertain system in the presence of disturbances and control input limits. Furthermore, to decrease the chattering phenomena, a genetic algorithm is used to optimize the controller parameters. Finally, numerical simulations are presented to demonstrate the performance of the designed control scheme in the presence of noise, disturbances, and control input saturation.

ACS Style

Shaojie Wang; Amin Yousefpour; Abdullahi Yusuf; Hadi Jahanshahi; Raúl Alcaraz; Shaobo He; Jesus M. Munoz-Pacheco. Synchronization of a Non-Equilibrium Four-Dimensional Chaotic System Using a Disturbance-Observer-Based Adaptive Terminal Sliding Mode Control Method. Entropy 2020, 22, 271 .

AMA Style

Shaojie Wang, Amin Yousefpour, Abdullahi Yusuf, Hadi Jahanshahi, Raúl Alcaraz, Shaobo He, Jesus M. Munoz-Pacheco. Synchronization of a Non-Equilibrium Four-Dimensional Chaotic System Using a Disturbance-Observer-Based Adaptive Terminal Sliding Mode Control Method. Entropy. 2020; 22 (3):271.

Chicago/Turabian Style

Shaojie Wang; Amin Yousefpour; Abdullahi Yusuf; Hadi Jahanshahi; Raúl Alcaraz; Shaobo He; Jesus M. Munoz-Pacheco. 2020. "Synchronization of a Non-Equilibrium Four-Dimensional Chaotic System Using a Disturbance-Observer-Based Adaptive Terminal Sliding Mode Control Method." Entropy 22, no. 3: 271.