Extinction in a nonautonomous competitive system with toxic substance and feedback control. (English) Zbl 1461.92096
Summary: This paper deals with a nonautonomous competitive system with infinite delays and feedback control. Sufficient conditions for the permanence of the system are first obtained. By constructing a suitable Lyapunov function, we obtain the sufficient conditions which guarantee that one of the components is driven to extinction. Our result shows that feedback control have an influence on the extinction of the system. Examples together with their numerical simulations illustrate the feasibility of our main results.
MSC:
| 92D25 | Population dynamics (general) |
| 92D40 | Ecology |
| 93B52 | Feedback control |
| 34K60 | Qualitative investigation and simulation of models involving functional-differential equations |
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