Abstract
In this study, the impulsive predator-prey dynamic systems on time scales calculus are studied. When the system has periodic solution is investigated, and three different conditions have been found, which are necessary for the periodic solution of the predator-prey dynamic systems with Beddington-DeAngelis type functional response. For this study the main tools are time scales calculus and coincidence degree theory. Also the findings are beneficial for continuous case, discrete case and the unification of both these cases. Additionally, unification of continuous and discrete case is a good example for the modeling of the life cycle of insects.
Highlights
The relationships between species and the outer environment, and the connections between different species are the description of the predator-prey dynamic systems which is the subject of mathematical ecology in biomathematics
In [20] [21], unification of the existence of periodic solutions of population models modelled by ordinary differential equations and their discrete analogues in form of difference equations, and extension of these results to more general time scales are studied
We investigate when the system has periodic solution
Summary
The relationships between species and the outer environment, and the connections between different species are the description of the predator-prey dynamic systems which is the subject of mathematical ecology in biomathematics. (2015) Impulsive Predator-Prey Dynamic Systems with Beddington-DeAngelis Type Functional Response on the Unification of Discrete and Continuous Systems. For nonautonomous case there are many studies about the existence of periodic solutions of predator-prey systems in continuous and discrete models based on the coincidence theory such as [4]-[12]. Some properties of the solution of predator-prey system with Beddington-DeAnglis type functional response and impulse impact are studied in [19] for continuous case. In [20] [21], unification of the existence of periodic solutions of population models modelled by ordinary differential equations and their discrete analogues in form of difference equations, and extension of these results to more general time scales are studied. In this paper we try to generalize periodic solutions of predator-prey dynamic systems with Beddington-DeAnglis type functional response and impulse to general time scales
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