Abstract
This paper presents a novel and simple three‐dimensional (3‐D) chaotic system by introducing two sine nonlinearities into a simple 3‐D linear dynamical system. The presented sine system possesses nine equilibrium points consisting of five index‐2 saddle foci and four index‐1 saddle foci which allow the coexistence of various types of disconnected attractors, also known as multistability. The coexisting multiple attractors are depicted by the phase plots and attraction basins. Coexisting bifurcation modes triggered by different initial values are numerically simulated by two‐dimensional bifurcation and complexity plots under two sets of initial values and one‐dimensional bifurcation plots under three sets of initial values, which demonstrate that the abundant coexisting multiple attractors’ behaviors in the presented sine system are related not only to the system parameters but also to the initial values. A simulation‐oriented circuit model is synthesized, and PSIM (power simulation) screen captures well validate the numerical simulations.
Highlights
A novel and simple 3-D sine chaotic system is presented. It has nine equilibrium points consisting of five index-2 saddle foci and four index-1 saddle foci, resulting in the coexistence of up to six types of disconnected attractors
Denote k1 k2 k and take k 3.6 and 5 as two examples. e values δ and σ of the equilibrium point E in (4) are the intersection points of two function curves h1 and h2 described by (5) and (6), as shown in Figures 1(a) and 1(b), respectively, from which nine pairs of δ and σ are obtained by inspecting the intersection points, indicating the existence of nine equilibrium points in the presented sine system
It can be concluded that due to the appearance of five index-2 saddle foci and four index-1 saddle foci and their interactions with each other, some disconnected attracting regions are thereby formed in the neighborhoods around these unstable saddle foci, resulting in the generation of coexisting multiple disconnected attractors
Summary
Numerous nonlinear dynamical systems have been reported that they present the coexistence of two or more disconnected attractors with their isolated attraction basins. Memristor-based circuits and systems with di erent types of equilibrium points are easy to exhibit coexisting attractors’ behaviors of multistability. Speaking, another bene cial and simple method for generating initial value o set-boosted coexisting attractors is to put periodic trigonometric functions into speci c o setboostable dynamical systems [37,38,39,40,41]. It has nine equilibrium points consisting of five index-2 saddle foci and four index-1 saddle foci, resulting in the coexistence of up to six types of disconnected attractors.
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