Aiming at an entangled-chaos system with a memristor, the dynamic analysis and circuit realization are studied. Combining with the quadratic flux-controlled memristor, a memristive chaotic system is constructed, and the multistable behavior of the system when the initial value of the system changes is studied by using the system phase diagram, bifurcation diagram, and Lyapunov exponent spectrum (LE). Spectral entropy (SE), C0, and SampEn are used to describe the complexity of the memristive entanglement-chaos system. Finally, the multistable behavior of the system is realized by the digital circuit chip STM32. The experimental results are consistent with the system analysis and the numerical simulation of the MATLAB software. The experimental results of the circuit provide a foundation for the engineering application of the system.

A new 3D offset-boostable symmetric system is proposed by an absolute value function introduced. The system seems to be more fragile and easier to the state of broken symmetry. Coexisting symmetric pairs of attractors get closer and closer, and finally get emerged together. Basins of attraction show how these coexisting attractors are arranged in phase space. All these coexisting attractors can be easily offset boosted in phase space by a single constant when the initial condition is revised accordingly. PSpice simulations prove all the phenomena.

In this paper, based on integer-order Hindmarsh–Rose (HR) neurons under an electric field, the fractional-order model is constructed, and the nonlinear term is decomposed by the Adomian decomposition method, and the numerical solution of the system is obtained. The firing behavior of the neuron model is analyzed by using a phase diagram, interspike interval (ISI) bifurcation diagram, sample entropy (SE) complexity, and largest Lyapunov exponent (LLE). Based on the sliding mode control theory, a chaos synchronization controller of the system is designed. Matlab simulation results show that the controller is realizable and effective, and also has the characteristic of fast response, which provides a reference for the control and application of a memristor neural network system.

This paper focuses on the FitzHugh-Nagumo (FHN) neuron system. We construct a three-dimensional memristive neuron system by introducing an exponential locally active memristor. The bias control of neurons is achieved by introducing bias constant terms or periodic functions into the system. Moreover, trigonometric functions and absolute value functions are used to respectively realize the self-replication and symmetrization of attractors as well as other regulations of multi-stable dynamic states. The initial conditions also exert an influence on the bias control of neurons. Meanwhile, we introduce a three-dimensional matrix rotating around the z-axis to implement rotation control. Analysis reveals that as the rotation angle θ varies from 0 to 2π, the offset of the neuron membrane potential undergoes periodic variations. Rotation control can alter the arrangement of attractors and enhance the performance of the neural network. The research findings offer a theoretical basis for understanding the dynamic behavior of neurons and developing new neural network models and hold potential value for assisting in the diagnosis of nervous system diseases.

In this research work, the time-delay problems existing in signal transmission and mechanical structures are considered, based on the fractional-order Lü chaotic system, a fractional - order Lü time-delay chaotic system is constructed. The frequency-domain method, Grunwald-Liouvile method, and Adomian decomposition method among the numerical solution methods for fractional-order systems are used to numerically solve the fractional-order time-delay system, and the numerical solutions of the fractional-order time-delay chaotic system are obtained and the corresponding phase diagrams are drawn. Through numerical solution, the bifurcation diagram, complexity, and attractor phase diagrams of the system are drawn, and the influence of parameters on the system is verified. The simulation results show that the fractional-order time-delay system has rich dynamic characteristics and differences among the three solution algorithms. Finally, the fractional-order time-delay chaotic circuit is designed and implemented based on the integer-order circuit using Laplace transform, and the 0.01- 0.99 order fractional-order Laplace transform expansion formula is given, which provides a theoretical basis for the study of more accurate fractional-order systems and circuit design.