Coexisting attractors, circuit realization and impulsive synchronization of a new four-dimensional chaotic system

Abstract

This paper presents a new four-dimensional chaotic system with three nonlinearities and two equilibria. The most striking feature of the new system is that it has different types of asymmetric coexisting attractors. Simulation experiments are used to study the complex dynamic behaviors of the system. The chaos, period-doubling bifurcation, coexisting attractors with respect to system parameters and initial values are found in the system. It shows that the system has coexisting chaotic attractors, coexisting periodic attractors, coexisting chaotic and periodic attractors. The electronic circuit is applied to implement the chaotic attractor and coexisting attractors for studying the physical significance of the system. In addition, we consider the synchronization of the system by using the impulsive control method. Some synchronization criteria are established via theoretical analysis and simulation example.

A New 4D Chaotic System with Two‐Wing, Four‐Wing, and Coexisting Attractors and Its Circuit Simulation

“…As b increases in [12,20], the bifurcation diagrams clearly show the trajectory of system (1) from classical period-doubling bifurcation to chaos. Table 1 shows the comparison of the Lyapunov exponents of the new system with the literature [12,[28][29][30]. It can be seen that the maximum LE 1 of the new system is larger.…”

“…In 2017, Lai et al proposed a unique 4D autonomous system with a signum function term [29], which can generate various types of coexisting attractors. In 2019, Zhou et al proposed a chaotic system with multiple asymmetric coexisting attractors [30] and carried out circuit simulation and pulse synchronization research.…”

Corrigendum: New numerical approach for fractional differential equations

“…Step-size (h) Error h = 1.0 0.5017 h = 0.1 0.0070 h = 0.01 0.0021 h = 0.001 0.0020 Figure 1: Numerical results for Caputo fractional problem (2) showing the comparison between the exact and approximate (numerical) results for t = 10. Take note of the variation in the amplitudes.…”

Dynamic Analysis and Finite-Time Synchronization of a New Hyperchaotic System With Coexisting Attractors

“…Studies have shown that the classic Lorenz and Rössler systems will generates coexisting attractors for some parameter regions [16], [17]. Some simple chaotic systems are also found to have coexisting attractors [18]- [24]. Some effective methods were put forward to construct an arbitrary number of coexisting attractors from simple chaotic systems [25], [26].…”