Synchronization of fractional order chaotic systems

The chaotic dynamics of fractional order systems begin to attract much attentions in recent years. In this brief report, we study the master-slave synchronization of fractional order chaotic systems. It is shown that fractional order chaotic systems can also be synchronized.Comment: 3 pages, 5 figure

Projective synchronization in fractional order chaotic systems and its control

The chaotic dynamics of fractional (non-integer) order systems have begun to attract much attention in recent years. In this paper, we study the projective synchronization in two coupled fractional order chaotic oscillators. It is shown that projective synchronization can also exist in coupled fractional order chaotic systems. A simple feedback control method for controlling the scaling factor onto a desired value is also presented.Comment: 6 pages, 2 figure

The effects of fractional order on a 3-D quadratic autonomous system with four-wing attractor.

Abstract: In this paper, a fractional 3-dimensional (3-D) 4-wing quadratic autonomous system (Qi system) is analyzed. Time domain approximation method (Grunwald–Letnikov method) and frequency domain approximationmethod are used together to analyze the behavior of this fractional order chaotic system. It is found that the decreasing of the system order has great effect on the dynamics of this nonlinear system. The fractional Qi system can exhibit chaos when the total order less than 3, although the regular one always shows periodic orbits in the same range of parameters. In some fractional order, the 4 wings are decayed to a scroll using the frequency domain approximation method which is different from the result using time domain approximation method. A surprising finding is that the phase diagrams display a character of local self-similar in the 4-wing attractors of this fractional Qi system using the frequency approximation method even though the number and the characteristics of equilibria are not changed. The frequency spectrums show that there is some shrinking tendency of the bandwidth with the falling of the system states order. However, the change of fractional order has little effect on the bandwidth of frequency spectrum using the time domain approximation method. According to the bifurcation analysis, the fractional order Qi system attractors start from sink, then period bifurcation to some simple periodic orbits, and chaotic attractors, finally escape from chaotic attractor to periodic orbits with the increasing of fractional order α in the interval [0.8, 1]. The simulation results revealed that the time domain approximation method is more accurate and reliable than the frequency domain approximation method

A locally active discrete memristor model and its application in a hyperchaotic map

© 2022 Springer Nature Switzerland AG. Part of Springer Nature. This is the accepted manuscript version of an article which has been published in final form at https://doi.org/10.1007/s11071-021-07132-5The 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.Peer reviewedFinal Accepted Versio

A New Chaotic System with Line of Equilibria: Dynamics, Passive Control and Circuit Design

A new chaotic system with line equilibrium is introduced in this paper. This system consists of five terms with two transcendental nonlinearities and two quadratic nonlinearities. Various tools of dynamical system such as phase portraits, Lyapunov exponents, Kaplan-Yorke dimension, bifurcation diagram and Poincarè map are used. It is interesting that this system has a line of fixed points and can display chaotic attractors. Next, this paper discusses control using passive control method. One example is given to insure the theoretical analysis. Finally, for the  new chaotic system, An electronic circuit for realizing the chaotic system has been implemented. The numerical simulation by using MATLAB 2010 and implementation of circuit simulations by using MultiSIM 10.0 have been performed in this study

Recent Advances and Applications of Fractional-Order Neural Networks

This paper focuses on the growth, development, and future of various forms of fractional-order neural networks. Multiple advances in structure, learning algorithms, and methods have been critically investigated and summarized. This also includes the recent trends in the dynamics of various fractional-order neural networks. The multiple forms of fractional-order neural networks considered in this study are Hopfield, cellular, memristive, complex, and quaternion-valued based networks. Further, the application of fractional-order neural networks in various computational fields such as system identification, control, optimization, and stability have been critically analyzed and discussed

Dynamic Behavior Analysis and Synchronization of Memristor-Coupled Heterogeneous Discrete Neural Networks

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).Continuous memristors have been widely studied in recent years; however, there are few studies on discrete memristors in the field of neural networks. In this paper, a four-stable locally active discrete memristor (LADM) is proposed as a synapse, which is used to connect a two-dimensional Chialvo neuron and a three-dimensional KTZ neuron, and construct a simple heterogeneous discrete neural network (HDNN). Through a bifurcation diagram and Lyapunov exponents diagram, the period and chaotic regions of the discrete neural network model are shown. Through numerical analysis, it was found that the chaotic region and periodic region of the neural network based on DLAM are significantly improved. In addition, coexisting chaos and chaos attractors, coexisting periodic and chaotic attractors, and coexisting periodic and periodic attractors will appear when the initial value of the LADM is changed. Coupled by a LADM synapse, two heterogeneous discrete neurons are gradually synchronized by changing the coupling strength. This paper lays a good foundation for the future analysis of LADMs and the related research of discrete neural networks coupled by LADMs.Peer reviewe