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On the way back to Knock airport we had time to squeeze in one last activity - a bird of prey free-flying demonstration at the Irish Raptor Research Centre in Ballymote.
Thus, the complete expression for the prey-free periodic solution of the system (1.3) is obtained.
Then the prey-free periodic solution is locally asymptotically stable if (3.4).
For the reason, it is necessary to consider the stability of the prey-free periodic solution.
It might be difficult to find out a necessary condition for the stability of the prey-free periodic solution.
From Theorem 3.2, we know that the prey-free periodic solution is locally asymptotically stable provided that.
Conditions for the stability of the prey-free positive periodic solution and for the permanence of the system are established via the Floquet theory and comparison theorem.
First of all, in order to study the extinction of the prey, the existence of a prey-free solution to the system (1.3) should be guaranteed.
In fact, we show the local stability of the prey-free periodic solution under some conditions and give a sufficient condition for the permanence of the system (1.3) by applying the Floquet theory.
Even if the Floquet theory is well known, we would like to mention the theory to study the stability of the prey-free periodic solution as a solution of the system (1.3).
For the extinction, we have found out a condition that the population of the prey goes to zero as time goes by via the study of the stability of a prey-free periodic solution.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com