This work proposes a new 5-D hyperchaotic system with a line of equilibrium points. The bifurcation properties of the new hyperchaotic system are analyzed using bifurcation diagrams and Lyapunov exponents spectra. Multistability and offset boosting properties of the new hyperchaotic system are also discussed. With the help of Multisim 14.0 circuit simulator, an electronic circuit design for the new 5-D hyperchaotic system with a line of equilibrium points has been constructed. Furthermore, an FPGA implementation of the proposed hyperchaotic system is performed by applying Forward Euler numerical methods using FPGA CYCLONE IV GX platform. Additionally, this study demonstrates the use of the Long-Short-Term Memory LSTM model to predict the future hyperchaotic behavior of the new 5-D hyperchaotic system. The Mean Square Error (MSE), Root Mean Square Error (RMSE), and the coefficient of determination (R²) metrics are used to evaluate the prediction performance of the proposed LSTM model. The small obtained values for MSE and RMSE respectively, along with R² scores near to 1, reveal the accuracy and reliability of the proposed prediction model.

In this paper, a new 3D chaotic dissipative system is introduced. Basics dynamical characteristics and properties are studied such as equilibrium points, Lyapunov exponent spectrum, Kaplan–Yorke dimension. Dynamics of the new 3D chaotic system is investigated also numerically using largest Lyapunov exponents spectrum and bifurcation diagrams. We derive new control results via adaptive control method based on Lyapunov stability theory and adaptive control theory for globally and exponentially synchronizing the identical 3-D novel chaotic systems with unknown system parameters. The results are validated by numerical simulation using Matlab.

In the recent years, significant research interest has been devoted in the modelling and applications of chaotic systems with stable equilibria. In this research study, we propose a new 3-D chaotic system with two stable node-foci equilibria and an unstable saddle-focus equilibrium. We conduct a detailed bifurcation analysis for the new chaotic system with the aid of bifurcation diagrams and Lyapunov exponents. We also show that the new chaotic system has multistability with coexisting attractors. Using MultiSim version 14.1, we design an electronic circuit for the proposed 3-D chaotic system. Finally, as an application, we introduce a voice cryptosystem using the new chaotic system with two stable node-foci equilibrium points and an unstable saddle-focus equilibrium point and its hardware realization on the FPGA platform.

In this paper, we investigated a three-dimensional chaotic system that models key aspects of a monetary system, including interest rates, investment demand, and price levels. The proposed system is described by a set of autonomous quadratic ordinary differential equations. We analyze the dynamic behavior of this system through equilibrium points and their stability, Lyapunov exponents (LEs), and bifurcation diagrams. The system demonstrates a variety of behaviors, including chaotic, periodic, and equilibrium states depending on parameter values. Additionally, we explore the multistability of the system and present a radial basis function neural network (RBFNN) controller design to stabilize the chaotic behavior. The effectiveness of the controller is validated through numerical simulations, highlighting its potential applications in economic and financial modeling.

In this article, we present a novel approach: a fractional-order fuzzy observer, an extension of the Thau-Luenberger observer, specifically designed for nonlinear systems characterized by commensurate non-integer order Takagi-Sugeno models. This work makes significant contributions in two key areas. Firstly, both the activation functions of the model and the Lipschitz fractional-order fuzzy observer are dependent on unmeasurable variables, particularly the system's state. Secondly, our proposed fuzzy observer explicitly incorporates the system's initial conditions. The stability conditions of the fractional-order fuzzy observer are expressed through Bilinear Matrix Inequalities, which are then converted into linear matrix inequalities (LMIs). Subsequently, numerical simulations are conducted to demonstrate the efficacy of our proposed estimator.

In this work, we present a new four-dimensional chaotic hyperjerk system with a half-line of equilibrium points. In the chaos literature, it is well-known that chaotic systems with an infinite number of equilibrium points exhibit hidden attractors. Thus, we deduce in this research work that the new chaotic hyperjerk system has hidden attractors. We next study the new chaotic hyperjerk system for a dynamic analysis using bifurcation plots and Lyapunov Exponents (LE) diagrams.We exhibit that the new hyperjerk system has a special property of multistability with coexisting attractors. Using Multisim version 14.2, we carry out an electronic circuit simulation for the proposed 4-D chaotic hyperjerk system with a half-line of equilibrium points. Finally, as an application in control engineering, we apply backstepping control for achieving antisynchronization of a pair of new chaotic hyperjerk systems taken as master-slave systems, which has important applications in communication systems.