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Bifurcation Analysis and Chaos Switchover Phenomenon in a Nonlinear Financial System with Delay Feedback

Yuting Ding

Department of Mathematics, Northeast Forestry University, Harbin 150040, P. R. China

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and

Jun Cao

College of Electromechanical Engineering, Northeast Forestry University, Harbin 150040, P. R. China

E-mail Address: zdhcj@126.com

Author for correspondence.

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https://doi.org/10.1142/S0218127415501655Cited by:8 (Source: Crossref)

Abstract

In this paper, we study the dynamics in delayed nonlinear financial system, with particular attention focused on Hopf and double Hopf bifurcations. Firstly, we identify the critical values for stability switches, Hopf and double Hopf bifurcations. We show how the parameters affect the dynamical behavior of the system. Secondly, the normal forms near the Hopf and double Hopf bifurcations, as well as the classifications of local dynamics are analyzed. These bifurcations lead a chaotic system to be stable states, such as the coexistence of a pair of stable equilibria or a pair of stable periodic oscillations, and then chaos disappears. Numerical simulations are presented to verify the analytical predictions. Furthermore, detailed numerical analysis using MATLAB extends the local bifurcation analysis to a global picture, namely, a family of stable periodic solutions exist in a large region of delay and “chaos switchover” phenomenon appears. Therefore, in accordance with the above theoretical analysis, reasonable parameters can be designed in order to achieve various applications.

Keywords:

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