Basin of Attraction Analysis of New Memristor‐Based Fractional‐Order Chaotic System

Abstract

Memristor is the fourth basic electronic element discovered in addition to resistor, capacitor, and inductor. It is a nonlinear gadget with memory features which can be used for realizing chaotic, memory, neural network, and other similar circuits and systems. In this paper, a novel memristor-based fractional-order chaotic system is presented, and this chaotic system is taken as an example to analyze its dynamic characteristics. First, we used Adomian algorithm to solve the proposed fractional-order chaotic system and yield a chaotic phase diagram. Then, we examined the Lyapunov exponent spectrum, bifurcation, SE complexity, and basin of attraction of this system. We used the resulting Lyapunov exponent to describe the state of the basin of attraction of this fractional-order chaotic system. As the local minimum point of Lyapunov exponential function is the stable point in phase space, when this stable point in phase space comes into the lowest region of the basin of attraction, the solution of the chaotic system is yielded. In the analysis, we yielded the solution of the system equation with the same method used to solve the local minimum of Lyapunov exponential function. Our system analysis also revealed the multistability of this system.

Implementation of the Simple Hyperchaotic Memristor Circuit with Attractor Evolution and Large-Scale Parameter Permission

“…Basin of attraction is an analytical method for studying the dynamical behavior of chaotic systems, and it can discriminate the types of attractors in which chaotic systems exhibit bounded behavior. Moreover, generating different regions of attraction indicates the existence of coexisting multistability [35][36][37]. By changing the initial values of any two variables within a certain range, while the initial values of other variables remain unchanged, the corresponding basins of attraction are obtained, as shown in Figure 20.…”

“…Meanwhile, the multistability of a chaotic system depends on the initial conditions of the system, and the basin of attraction is a method to analyze the multistability of a chaotic system. The dynamic behavior of the system can be well distinguished according to the different attraction regions of the basin of attraction [31,[34][35][36][37]. With the in-depth study of memristor chaotic circuits, analog memristor circuits are easily affected by the external environment, while FPGA technology has the advantages of high flexibility, parallel computing, low power consumption and high reliability [38,39].…”

Nonlinear coexistence phenomenon and FPGA implementation with the hybrid of memristive–memcapacitive hyperchaotic system

“…This method selects two sensitive initial values in the system as variables to draw a color map. Different colors in the map represent that the system is in different states [29]. In the attractive basin, in addition to the invariant manifold, there will be different bifurcations and different forms of attractive basin [30].…”

Coexisting Attractor in a Gyrostat Chaotic System via Basin of Attraction and Synchronization of Two Nonidentical Mechanical Systems

“…Basins can also play a helpful role in finding hidden and coexisting attractors in chaotic systems [20][21][22][23]. The coexisting attractor (multistability) [24] for a set of parameters has been studied for many nonlinear systems.…”