Abstract
A problem of the analysis and prevention of noise-induced extinction in nonlinear population models is considered. For the solution of this problem, we suggest a general approach based on the stochastic sensitivity analysis. To prevent the noise-induced extinction, we construct feedback regulators which provide a low stochastic sensitivity and keep the system close to the safe equilibrium regime. For the demonstration of this approach, we apply our mathematical technique to the conceptual but quite representative Ricker-type models. A variant of the Ricker model with delay is studied along with the classic widely used one-dimensional system.
Highlights
Population models, even in the deterministic case, demonstrate a wide variety of dynamic regimes, both equilibrium and oscillatory
In the modern population dynamics, along with the problem of the analysis of unwanted shifts caused by noise, control problems for ecosystems are highly important
We studied the noise-induced extinction in nonlinear population models
Summary
Population models, even in the deterministic case, demonstrate a wide variety of dynamic regimes, both equilibrium and oscillatory. These regular and chaotic regimes can be changed in consequence of the different-type bifurcations [1, 2]. We use the Ricker system as a conceptual model to study the probabilistic mechanisms of phenomena of the noise-induced extinction and contraction of the persistence zone. We use a control approach oriented on the Discrete Dynamics in Nature and Society synthesis of the stable equilibrium with the small stochastic sensitivity. We demonstrate how the mathematical theory of the stochastic sensitivity synthesis can be applied to the systems of higher dimensions
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