Symmetric Coexisting Attractors in a Novel Memristors-Based Chuas Chaotic System

This paper introduces a charge-controlled memristor based on the classical Chuas circuit. It also designs a novel four-dimensional chaotic system and investigates its complex dynamics, including phase portrait, Lyapunov exponent spectrum, bifurcation diagram, equilibrium point, dissipation and stability. The system appears as single-wing, double-wings chaotic attractors and the Lyapunov exponent spectrum of the system is symmetric with respect to the initial value. In addition, symmetric and asymmetric coexisting attractors are generated by changing the initial value and parameters. The findings indicate that the circuit system is equipped with excellent multi-stability. Finally, the circuit is implemented in Field Programmable Gate Array (FPGA) and analog circuits.

Design and Analysis of a Three-Dimensional Discrete Memristive Chaotic System with Infinite Wide Parameter Range

In this paper, a new discrete memristive chaotic system with infinitely wide parameter range is designed. Firstly, a discrete memristor based on a triangular wave function is constructed. The memristor conforms to the definition of generalized memristor, and a new three-dimensional memristive chaotic system is designed based on it. Numerical simulations show that it can generate chaotic sequences with high complexity.Otherwise, an improved perturbation method is proposed to estimate the output sequence of the differential system. At the same time, it is proved mathematically that the new system can always be in chaotic or hyperchaotic state with infinitely wide parameter range under certain conditions. By observing the Lyapunov exponent spectrum and the phase diagram, it is found as the absolute value of the parameter increases, the output range and ergodicity of the new system are also enhanced, and the new system has super multi-stability. This paper analyzes the mechanism of the discrete memristive chaotic system generating infinitely coexisting attractors, puts forward a method to make ordinary chaotic systems easier to obtain super multi-stability, and verifies it. The results show it is effective. Finally, the DSP hardware platform is used to implement the new system, which proves the physical existence and realizability of the system.

A locally Active Discrete Memristor Model and Its Application in a Hyperchaotic Map

The continuous memristor is a popular topic of research in recent years, however, there is rare discussion about the discrete memristor model, especially the locally active discrete memristor model. This paper proposes a locally active discrete memristor model for the first time and proves the three fingerprints characteristics of this model according to the definition of generalized memristor. A novel hyperchaotic map is constructed by coupling the discrete memristor with a two-dimensional generalized square map. The dynamical behaviors are analyzed with attractor phase diagram, bifurcation diagram, Lyapunov exponent spectrum, and dynamic behavior distribution diagram. Numerical simulation analysis shows that there is significant improvement in the hyperchaotic area, the quasi-periodic area and the chaotic complexity of the two-dimensional map when applying the locally active discrete memristor. In addition, antimonotonicity and transient chaos behaviors of system are reported. In particular, the coexisting attractors can be observed in this discrete memristive system, resulting from the different initial values of the memristor. Results of theoretical analysis are well verified with hardware experimental measurements. This paper lays a great foundation for future analysis and engineering application of the discrete memristor and relevant the study of other hyperchaotic maps.

Dynamics Analysis and Synchronous Control of Fractional-Order Entanglement Symmetrical Chaotic Systems

In this paper, the Adomian decomposition method (ADM) semi-analytical solution algorithm is applied to solve a fractional-order entanglement symmetrical chaotic system. The dynamics of the system are analyzed by the Lyapunov exponent spectrum, bifurcation diagrams, poincaré diagrams, and chaos diagrams. The results show that the systems have rich dynamics. Meanwhile, sliding mode synchronizations of fractional-order chaotic systems are investigated theoretically and numerically. The results show the effectiveness of the proposed method and potential application value of fractional-order systems.

Comparison of Complexity of the Switchable Chaotic Systems and its FPGA Implementation

A four-dimensional chaotic system with complex dynamical properties is constructed via introducing a nonlinear function term. The paper assesses complexity of the system employing equilibrium points, Lyapunov exponent spectrum and bifurcation model. Specially, the coexisting Lyapunov exponent spectrum and the coexisting bifurcation validate the coexistence of attractors. The corresponding complexity characteristics of the system can be analyzed by using C0 and spectral entropy(SE) complexity algorithms, and the most complicated integer-order system is obtained. Furthermore, the circuit which can switch the chaotic attractors is implemented. It is worth noting that the more sophisticated parameters are received by comparing the complexity of the most complicated integer-order chaotic system with corresponding fractional-order chaotic system. Finally, the results of simulation model built in the MATLAB are the same as the hardware verified on the Field-Programmable Gate Array(FPGA) platform, which verify the feasibility of the system.

A Simple Parallel Chaotic Circuit Based on Memristor

This paper reports a simple parallel chaotic circuit with only four circuit elements: a capacitor, an inductor, a thermistor, and a linear negative resistor. The proposed system was analyzed with MATLAB R2018 through some numerical methods, such as largest Lyapunov exponent spectrum (LLE), phase diagram, Poincaré map, dynamic map, and time-domain waveform. The results revealed 11 kinds of chaotic attractors, 4 kinds of periodic attractors, and some attractive characteristics (such as coexistence attractors and transient transition behaviors). In addition, spectral entropy and sample entropy are adopted to analyze the phenomenon of coexisting attractors. The theoretical analysis and numerical simulation demonstrate that the system has rich dynamic characteristics.

A New 4D Piecewise Linear Multiscroll Chaotic System with Multistability and Its FPGA-Based Implementation

Due to the complex behavior of a multiscroll chaotic system, it is a good candidate for the secure communications. In this paper, by adding an additional variable to the modified Lorenz-type system, a new chaotic system that includes only linear and piecewise items but can generate 4n + 4 scroll chaotic attractors via choosing the various values of natural number n is proposed. Its dynamics including bifurcation, multistability, and symmetric coexisting attractors, as well as various chaotic and periodic behaviors, are analyzed by means of attraction basin, bifurcation diagram, dynamic map, phase portrait, Lyapunov exponent spectrum, and C0 complexity in detail. The mechanism of the occurrence for generating multiscroll chaotic attractors is presented. Finally, this multiscroll chaotic system is implemented by using the Altera Cyclone IV EP4CE10F17C8 FPGA. It is found that this FPGA-based design has an advantage of requiring less resources for 0% of the embedded multipliers and 0% of the PLLs of this FPGA are occupied.

Construction of a Class of High-Dimensional Discrete Chaotic Systems

In this paper, a class of n-dimensional discrete chaotic systems with modular operations is studied. Sufficient conditions for transforming this kind of discrete mapping into a chaotic mapping are given, and they are proven by the Marotto theorem. Furthermore, several special systems satisfying the criterion are given, the basic dynamic properties of the solution, such as the trace diagram and Lyapunov exponent spectrum, are analyzed, and the correctness of the chaos criterion is verified by numerical simulations.

Periodic Motion and Transition of a Vibro‐Impact System with Multilevel Elastic Constraints

In this paper, a single-degree-of-freedom vibroimpact system with multilevel elastic constraints is taken as the research object. By constructing the Poincaré map of the system and calculating the Lyapunov exponent spectrum of the system, the stability of the system is determined. Using the multiparameter collaborative numerical simulation method, the parameter domains of various periodic motions are determined, and the diversity and transition characteristics of periodic motions are revealed. At the same time, combined with the cell mapping method, the coexistence of attractors induced due to grazing bifurcation, saddle-node bifurcation, and boundary crisis is studied. Finally, the influence of system parameters on periodic motion distribution is analyzed, which provides a scientific basis for system parameter optimization.

Design of 9-D global chaotic system and its application in secure communication

Purpose In this paper, a nine-dimensional chaotic system is designed and applied to secure communication. Design/methodology/approach Firstly, the equilibrium characteristics, dissipativity, bifurcation diagram and Lyapunov exponent spectrum are used to analyze the relevant characteristics of the proposed nine-dimensional chaotic system. In the analysis of Lyapunov exponential spectrum, when changing the linear parameters, the system shows two states, hyperchaos and chaos. For secure communication, there is a large secret key space. Secondly, C0 complexity and SEcomplexity of the system are analyzed, which shows that the system has sequences closer to random sequences. Findings The proposed nine-dimensional system has a large key space and more complex dynamic characteristics Originality/value The results show that the proposed nine-dimensional hyperchaotic system has excellent encryption capabilities and can play an important role in the field of secure communication.