## Feedback control has no influence on the persistent property of a single species discrete model with time delays.(English)Zbl 1235.93113

Summary: By developing some new analysis techniques, we show that the following discrete single species model with feedback control and time delays is permanent. $\begin{cases} N(n+1)=N(n)\exp\{r(n)[1-\frac{N^2(n-m)}{k^2(n)}-c(n)u(n-\eta)]\}\\\Delta(u)=-a(n)u(n)+b(n)N(n-\sigma), \end{cases},$ where $$N(n)$$ is the density of species, $$u(n)$$ is the control variable, $$\Delta$$ is the first-order forward difference operator $$\Delta u(n)=u(n+1)-u(n)$$. $$m,\sigma ,\eta$$ are all nonnegative integers and $$r(n), a(n), k(n), c(n), b(n), d(n)$$ are bounded nonnegative sequences. Our result shows that feedback control has no influence on the persistent property of the system.

### MSC:

 93B52 Feedback control 92D25 Population dynamics (general) 39A22 Growth, boundedness, comparison of solutions to difference equations

### Keywords:

nonautonomous; permanence; feedback control; time delays
Full Text:

### References:

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