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Title of Journal: Nonlinear Dyn

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Abbravation: Nonlinear Dynamics

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Springer Netherlands

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DOI

10.1007/s12039-011-0137-9

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1573-269X

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Bifurcation analysis and circuit realization for m

Authors: Zhouchao Wei VietThanh Pham Tomasz Kapitaniak Zhen Wang
Publish Date: 2016/04/22
Volume: 85, Issue: 3, Pages: 1635-1650
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Abstract

In this paper we investigate the effect of multiple delays on the 3D simple chaotic system with hidden chaotic attractors coexisting with one stable equilibrium by Wang and Chen In order to investigate complex dynamics of hidden chaotic attractors with multiple delays we choose tau 1 and tau 2 as bifurcating parameters and consider the stability of equilibrium and the existence of Hopf bifurcations Some explicit formulas for determining the direction of bifurcations and the stability of bifurcating periodic solutions are obtained by using normal form theory and center manifold theory The numerical simulations are performed to support the correctness and effectiveness of the analytical results The effect of multiple delays can be applied to the chaotic system only with one stable nodefoci for the purpose of control and anticontrol of hidden chaos by delayed switchover Furthermore to reach deep and clear understanding of the dynamics of such hidden attractors circuit implementation of the multiple timedelay system is analyzed using the PSpiceWe would like to express our gratitude to the referee for his or her valuable comments and suggestions that led to a truly significant improvement of the manuscript This work was supported by the Polish National Science Centre MAESTRO Programme—Project No 2013/08/A/ST8/00/780 the Natural Science Foundation of China No 11401543 the China Scholarship Council CSC No 201506415023 Beijing Postdoctoral Research Foundation No 2015ZZ17 the China Postdoctoral Science Foundation funded project Nos 2014M560028 and 2015T80029 the Fundamental Research Funds for the Central Universities China University of Geosciences Wuhan No CUGL150419 the Natural Science Foundation of Hubei Province No 2014CFB897 the Government of Chaoyang District Postdoctoral Research Foundation No 2015ZZ7 and the Funding Project for Academic Human Resources Development in Institutions of Higher Learning under the Jurisdiction of Beijing Municipality PHRIHLB

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