Stochastic bifurcation in a model of love with colored noise

Xiaokui Yue (), Honghua Dai and Jianping Yuan
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Xiaokui Yue: School of Astronautics, Northwestern Polytechnical University, Xi'an 710072, P. R. China
Honghua Dai: School of Astronautics, Northwestern Polytechnical University, Xi'an 710072, P. R. China
Jianping Yuan: School of Astronautics, Northwestern Polytechnical University, Xi'an 710072, P. R. China

International Journal of Modern Physics C (IJMPC), 2015, vol. 26, issue 02, 1-11

Abstract: In this paper, we wish to examine the stochastic bifurcation induced by multiplicative Gaussian colored noise in a dynamical model of love where the random factor is used to describe the complexity and unpredictability of psychological systems. First, the dynamics in deterministic love-triangle model are considered briefly including equilibrium points and their stability, chaotic behaviors and chaotic attractors. Then, the influences of Gaussian colored noise with different parameters are explored such as the phase plots, top Lyapunov exponents, stationary probability density function (PDF) and stochastic bifurcation. The stochastic P-bifurcation through a qualitative change of the stationary PDF will be observed and bifurcation diagram on parameter plane of correlation time and noise intensity is presented to find the bifurcation behaviors in detail. Finally, the top Lyapunov exponent is computed to determine the D-bifurcation when the noise intensity achieves to a critical value. By comparison, we find there is no connection between two kinds of stochastic bifurcation.

Keywords: Stochastic bifurcation; love model; Gaussian colored noise; stationary probability density (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1142/S0129183115500217

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