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PresentationsAllee effect influence on the dynamics of the stochastic Ricker population model with migrationsUral Federal University This paper considers a stochastic model consisting of two coupled subsystems, which is modeled by a discrete Ricker mapping first described in [1]. Bifurcation diagrams have been plotted for the deterministic version of the model and the case when both populations are in equilibrium regimes has been selected for study. The parameter zones at which multistability of the system is observed were found and described. The stability of the attractors of the system is illustrated using Lyapunov exponent. Basins of the attractors for the zones of coexistence of several attractors of the system are studied. Various oscillation scenarios are described. For the stochastic case the behavior of the attractors of the system depending on the intensity of the introduced parametric noise is described. Noise induced transitions between attractors are described for cases where multistability is observed. The stochastic sensitivity function method [2] is used for the analysis, which allows us to describe the response of the system to the introduced noise. Critical values of noise intensity were found at which both complete and partial extinction of populations is observed. [1] E. W. Ricker. Stock and recruitment. Journal of the Fisheries Research Board of Canada, 11: 5 (1954), 559–623. [2] Bashkirtseva, I., Ryashko, L., Tsvetkov, I. Sensitivity analysis of stochastic equilibria and cycles for discrete dynamic systems // Dyn. Contin., Discrete Impulsive Syst. Ser. A 17, 2010. 501–515.
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