Dynamic properties for a stochastic food chain model. (February 2022)

• Record Type: Journal Article
• Authors: Zou, Xiaoling; Ma, Pengyu; Zhang, Liren; Lv, Jingliang
• Is Part Of: Chaos, solitons and fractals. Volume 155(2022)
• Publication Date: 2022-02
• Subjects: Holling type II functional response -- Intra-specific competition -- Lyapunov exponent -- Survival and extinction threshold -- Stochastic dynamical bifurcation; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2021.111713
• Languages: English
• ISSNs: 0960-0779

Abstract

Highlights: Stochastic models can also satisfy Ayala's experimental results, or rather, competitive coexistence is possible in the random case. There are five points of dynamical bifurcation for the considered stochastic model. Each of the five bifurcation points has special biological significance. The survival and extinction thresholds of the whole system as well as each species are analyzed in this paper. Environmental noise can drive the system towards extinction from partial extinction or coexistence. This article suggests a new meshing method, which can test Lyapunov exponents for two-dimensional boundary measures. Theoretical results are verified nicely by numerical simulations. Abstract: In this paper, Lyapunov exponents of ergodic invariant measures are used to study dynamic properties for a stochastic food chain model, which consists of two competing predators and one prey. Ayala's experimental result, or rather, competitive coexistence is showed to be possible in this random case. Furthermore, the considered stochastic model have five points of dynamical bifurcation, which happen to be the thresholds (between survival and extinction) of the system or each species. In addition, the necessity of introducing environmental noise is verified by the fact that environmental driving force can drive the system towards extinction from partial extinction or coexistence. Moreover, all the theoretical results are well verified by numerical simulations. It is worth mentioning that we make a first attempt at using meshing method and statistical data to test Lyapunov exponents for two-dimensional boundary measures, and this is an innovation in the numerical methods.