Hidden attractors, singularly degenerate heteroclinic orbits, multistability and physical realization of a new 6D hyperchaotic system

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Detail(s)

Original languageEnglish
Article number105362
Number of pages16
Journal / PublicationCommunications in Nonlinear Science and Numerical Simulation
Volume90
Online published28 May 2020
Publication statusPublished - Nov 2020

Abstract

This paper reports a sequential design of linearly controlling a three-dimensional (3D) quadratic system to a simple six-dimensional hyperchaotic system with complex dynamics. By adding three linear dynamical controllers, the resulting 6D system has no equilibrium and a hidden attractor, which has four positive Lyapunov exponents (LEs). This paper focuses on the 6D system, to reveal its unusual dynamics such as infinitely many singularly degenerate heteroclinic cycles and bifurcations from such singular orbits to hidden hyperchaotic attractors. Detailed numerical investigations are carried out, including bifurcation diagram, LE spectrum and phase portrait. Furthermore, the system has multistability corresponding to three types of equilibria, including no equilibrium and infinite non-isolated equilibria. In particular, we find that at least seven different attractors coexist when the system has one equilibrium line. Finally, this 6D hyperchaotic system is verified by 0–1 test and a circuit.

Research Area(s)

  • Chaos and hyperchaos, Hidden attractor, Multistability, Singularly degenerate heteroclinic orbit

Citation Format(s)

Hidden attractors, singularly degenerate heteroclinic orbits, multistability and physical realization of a new 6D hyperchaotic system. / Yang, Lingbing; Yang, Qigui; Chen, Guanrong.

In: Communications in Nonlinear Science and Numerical Simulation, Vol. 90, 105362, 11.2020.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review