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Dynamical model of a single-species system in a polluted environment. (English) Zbl 1052.92056

Summary: The effect of toxicants on ecological systems is an important issue from mathematical and experimental points of view. We have studied a dynamical model of a single-species population-toxicant system. Two cases are studied: constant exogeneous input of toxicant and rapidly fluctuating random exogeneous input of toxicant into the environment. The dynamical behaviour of the system is analyzed by using deterministic linearized techniques, Lyapunov method and stochastic linearization on the assumption that exogeneous input of toxicants into the environment behaves like ‘coloured noise’.

MSC:

92D40 Ecology
37N25 Dynamical systems in biology
92D25 Population dynamics (general)
34D23 Global stability of solutions to ordinary differential equations
60G35 Signal detection and filtering (aspects of stochastic processes)
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