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Impact of two types of time delays and cross-correlated multiplicative and additive noises on stability and stochastic resonance for a metapopulation system

Author

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  • Wang, Kang-Kang
  • Zong, De-Cai
  • Li, Sheng-Hong
  • Wu, Jian-Cheng

Abstract

In this paper, we investigate the stability and the shift between the extinction state and the stable one of a large density and the stochastic resonance (SR) for a metapopulation system subjected to two types of time delay terms, cross-correlation noises and multiplicative signal. By using the fast descent method and the method of small delay approximation, the expressions of the effective potential function and the signal-to-noise ratio (SNR) are obtained. We denote by Q the intensity of the multiplicative noise, and M the intensity of the additive noise, θ and τ the two time delay terms introduced into the metapopulation system. Our main results show some facts that time delay θ and the strength of correlation noise λ can restrain the development of the metapopulation, while the other term of time delay τ can accelerate the expansion of the population from the extinction state to the large stable one. We discover that it is possible to enhance the signal-to-noise ratio by adjusting the intensities of the multiplicative, additive noises and the time delays of the stochastic metapopulation system

Suggested Citation

  • Wang, Kang-Kang & Zong, De-Cai & Li, Sheng-Hong & Wu, Jian-Cheng, 2016. "Impact of two types of time delays and cross-correlated multiplicative and additive noises on stability and stochastic resonance for a metapopulation system," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 235-247.
    • Handle: RePEc:eee:chsofr:v:91:y:2016:i:c:p:235-247
    DOI: 10.1016/j.chaos.2016.06.003
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