Stochastic delayed dynamics for a metapopulation system induced by non-Gaussian noise and a multiplicative periodic sign
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ORIGINAL PAPER
Stochastic delayed dynamics for a metapopulation system induced by non-Gaussian noise and a multiplicative periodic signal K-K Wang1,3*, D-C Zong2, Y-J Wang1 and S-H Li4 1
School of Science, Jiangsu University of Science and Technology, Zhenjiang 212003, China
2
College of Computer Science and Engineering, Changshu Institute of Technology, Changshu 215500, China
3
Center of Complex Systems and Network Science Research, Southeast University, Nanjing 210096, China 4
School of Mathematical Sciences, Nanjing Normal University, Nanjing 210097, China Received: 10 August 2019 / Accepted: 25 May 2020
Abstract: In this paper, we focus on shedding light on the stochastic stability, the MFPT and stochastic resonance (SR) phenomena for a metapopulation system in the presence of time delay, the colored cross-correlated multiplicative nonGaussian noise and the additive Gaussian colored noise. By use of the fast descent method and the approximation of the unified colored noise, the dynamical behaviors for the modified potential function and the signal-to-noise ratio (SNR) are analyzed in detail. It is discovered that the additive Gaussian colored noise, the noise correlation strength as well as its selfcorrelation time can all impair the stability of the population system and speed up the population decline. Conversely, the two self-correlation times of the external and internal noises can both consolidate the stability of the biological system and prolong the survival time of the population. With regard to the SNR for the metapopulation system caused by the noise terms and time delay, it is revealed that time delay, the noise correlation strength and its correlation time can all along weaken the SR phenomenon. On the contrary, two noise self-correlation times are able to amplify effectively the resonance effect. It is worth noting that the parameter of non-Gaussianity q in the SNR-s and SNR-k plots can initially weaken the SR phenomena and then enhance the maximum of the SNR as it is further increased. Keywords: Non-Gaussian noise; Metapopulation system; Time delay; Departure from the Gaussian noise; Mean extinction time
1. Introduction In the several decades, a great number of investigation results in regard to noise have leaded us to be convinced that noise can play a determinative part in a variety of areas [1–5], for example ecology [6–8], biology [9–12], chemistry [13, 14], physics [15, 16] and so on. In particular, the noise has been well thought of as a significant factor in population systems [17–20]. The scholars have explored many noise-induced phenomena, such as noise-induced shift in honeybee foraging dynamics [21], noise-induced adaptive decision making in dynamic environments [22] and the spontaneous formation of species [23] caused by the demographic noise, etc. The noise and determinism
*Corresponding author, E-mail: [email protected]
have been further investigated in synchronous sheep dynamics [24]. Scientists have discovered a fact that noise not only results in a transition between stea
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