Hidden attractors from the switching linear systems

Abstract

Recently, chaotic behavior has been studied in dynamical systems that generates hidden attractors. Most of these systems have quadratic nonlinearities. This paper introduces a new methodology to develop a family of three-dimensional hidden attractors from the switching of linear systems. This methodology allows to obtain strange attractors with only one stable equilibrium, attractors with an infinite number of equilibria or attractors without equilibrium. The main matrix and the augmented matrix of every linear system are considered in Rouché-Frobenius theorem to analyze the equilibrium of the switching systems. Also, a systematic search assisted by a computer is used to find the chaotic behavior. Basic chaotic properties of the attractors are verified by the Lyapunov exponents.

Proposing and Dynamical Analysis of a Hyperjerk Piecewise Linear Chaotic System with Offset Boostable Variable and Hidden Attractors

“…PWL systems mostly consist of two or more affine functions. ese affine functions provide the situation in which adding more equilibria and switching surfaces provide multiscroll attractors [34,37]. Although, in the proposed system, a general case was considered with nonlinear terms that empower the attractors' complexity, this claim can be confirmed by comparing the bifurcation diagrams derived from both these subgroups of PWL systems.…”

“…Chua's system is one of the most popular PWL systems, which shows chaotic behavior [35]. Different PWL systems have been proposed with multiscroll chaotic attractors and different numbers of equilibria [36,37]. Primarily, polynomial approaches have been used to generate such chaotic attractors [38,39].…”

Dynamics analysis of memristor chaotic circuit with coexisting hidden attractors

“…Another kind of attractor newly proposed in recent years was called hidden attractor, whose basin does not intersect with the small neighborhood of any equilibrium points. The coexisting attractors and hidden attractors are of considerable importance in nonlinear dynamics and engineering applications [26][27][28][29][30][31][32]. In Ref.…”