Periodic solutions in a delayed predator-prey model with nonmonotonic functional response. (English) Zbl 1176.34103
Authors’ abstract: “By using the continuation theorem of coincidence degree theory, the existence of a positive periodic solution for a delayed predator-prey model with nonmonotonic functional response
\[ \begin{cases} x'(t) = x(t)(a(t)-b(t)x(t))-(x(t)y(t))/(m^2+cx(t)+x^2(t)), \\ y'(t) = y(t)(\mu(t)x(t-\tau))/(m^2+cx(t-\tau)+x^2(t-\tau))-d(t)), \end{cases} \]
is established, where \(a(t)\), \(b(t)\), \(\mu(t)\) and \(d(t)\) are all positive periodic continuous functions with period \(\omega>0\), \(c>0\), \(m>0\) and \(\tau\) is a nonnegative constant. In particular, our result improves a former conclusion.”
\[ \begin{cases} x'(t) = x(t)(a(t)-b(t)x(t))-(x(t)y(t))/(m^2+cx(t)+x^2(t)), \\ y'(t) = y(t)(\mu(t)x(t-\tau))/(m^2+cx(t-\tau)+x^2(t-\tau))-d(t)), \end{cases} \]
is established, where \(a(t)\), \(b(t)\), \(\mu(t)\) and \(d(t)\) are all positive periodic continuous functions with period \(\omega>0\), \(c>0\), \(m>0\) and \(\tau\) is a nonnegative constant. In particular, our result improves a former conclusion.”
Reviewer: Yuming Chen (Waterloo)
MSC:
| 34K60 | Qualitative investigation and simulation of models involving functional-differential equations |
| 34K13 | Periodic solutions to functional-differential equations |
| 92D25 | Population dynamics (general) |
| 47N20 | Applications of operator theory to differential and integral equations |
Keywords:
predator-prey model; nonmonotonic functional response; periodic solution; coincidence degree; delayReferences:
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