Multiscroll attractors by switching systems

Abstract

In this paper, we present a class of three-dimensional dynamical systems having multiscrolls which we call unstable dissipative systems (UDSs). The UDSs are dissipative in one of its components but unstable in the other two. This class of systems is constructed with a switching law to display various multiscroll strange attractors. The multiscroll strange attractors result from the combination of several unstable "one-spiral" trajectories by means of switching. Each of these trajectories lies around a saddle hyperbolic stationary point. Thus, we describe how a piecewise-linear switching system yields multiscroll attractors, symmetric or asymmetric, with chaotic behavior.

Grayscale image encryption using a hyperchaotic unstable dissipative system

“…Based on the piece-wise linear (PWL) systems concept along ideas presented in [12], [l3], let us consider here the class of afine linear system given as: ii) Type II: Two of Ai are negative real eigenvalues, and two of Ai are complex conjugate eigenvalues with positive real part Re{Ad > O. Both these types result in a saddle equilibrium point X*.…”

Attractors generated from switching unstable dissipative systems

“…2 The saddle points of a chaotic system in R 3 can be characterized into two types according to its eigenvalues K ¼ fk i ; k j ; k k g 2 C: (i) The saddle points that are stable in one of its components but unstable or oscillatory in the other two. 3 That is, the stable component is corresponding to a negative real eigenvalue; i.e., Refk i g < 0; Imfk i g ¼ 0, whereas the unstable components are related with two complex conjugate eigenvalues; i.e., Refk k g > 0, Imfk k g 6 ¼ 0. (ii) The saddle points that are stable in two of its components but unstable in the another one.…”

“…In general, chaotic dynamical systems have been constructed in two options: (i) considering both UDS Type I and Type II, for example Chua's systems; or (ii) only using UDS Type I, as those reported in Ref. 3.…”

Chaos Entanglement: A New Approach to Generate Chaos

“…Chaos entanglement with piecewise linear function can be thought of as a switching linear system, but it is definitely new, different from the one in [Campos-Cantón et al, 2010]. For instance, et al, 2010].…”