On the analysis of local bifurcation and topological horseshoe of a new 4D hyper-chaotic system

Leilei Zhou, Zengqiang Chen, Zhonglin Wang and Jiezhi Wang

Chaos, Solitons & Fractals, 2016, vol. 91, issue C, 148-156

Abstract: In this paper, a new four-dimensional (4D) smooth quadratic autonomous system with complex hyper-chaotic dynamics is presented and analyzed. The Lyapunov exponent (LE) spectrum, bifurcation diagram and various phase portraits of the system are provided. The stability, Hopf bifurcation and pitchfork bifurcation of equilibrium point are discussed by using the center manifold theorem and bifurcation theory. Numerical simulation results are consistent with the theoretical analysis. Besides, by combining the topological horseshoe theory with a computer-assisted method of Poincaré maps and utilizing the algorithm for finding horseshoes in 3D hyper-chaotic maps, a horseshoe with two-directional expansions in the 4D hyper-chaotic system is successfully found, which rigorously proves the existence of hyper-chaos in theory.

Keywords: Chaos; Hyper-chaos; Hopf bifurcation; Pitchfork bifurcation; Topological horseshoe (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:91:y:2016:i:c:p:148-156

DOI: 10.1016/j.chaos.2016.05.017

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