Abstract
In this paper, we consider an integral equation of Fredholm type that describes the dynamics of a Daphnia population that is also coupled with an integro-differential equation, which describes the dynamics of algae, and incorporates the effects of the Daphnia population feeding on them. We determine the steady states of the above mentioned coupled system of equations. Basically, there are three types of steady states: first, is the trivial steady state, where both the Daphnia population and algae vanish. Second, is the case when the Daphnia population vanishes and algae at the carrying capacity. Third, is the case where both the Daphnia population and algae coexist. Our main purpose in this paper is to provide stability results for the steady states, via analyzing the characteristic equation of the coupled system of equations, which is also obtained previously in [1], and its analysis is thought to be involved, prohibitive and unattainable. The trivial steady state is unstable, whereas the steady where the Daphnia population vanishes and algae at the carrying capacity, is locally asymptotically stable if a specified condition is satisfied, otherwise, is unstable. The nontrivial steady state, where both the Daphnia population and algae coexist, is locally asymptotically stable under a given condition.
References
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How to cite this paper
Stability Analysis of a Population Dynamics Model of Daphnia
How to cite this paper: M. El-Doma. (2022) Stability Analysis of a Population Dynamics Model of Daphnia. Journal of Applied Mathematics and Computation, 6(4), 454-457.
DOI: http://dx.doi.org/10.26855/jamc.2022.12.007