Dynamical study of a prey–predator system with a commensal species competing with prey species: effect of time lag and alternative food source
Tóm tắt
In the present paper, we have studied a model for three species system with time lag considering two competing species and a predator species which is partially coupled with an alternative prey. It is also considered in the model that one of the competing population (commensal species) is supported by the predator species (host species). All the equilibrium points of the model are derived which are studied using stability and bifurcation theory. It is shown that the equilibrium levels of all the species increase or decrease with respect to alternative food source constant
$$A$$
. It is also shown in the paper that introduction of the delay in the system exhibits Hopf bifurcation. Numerical Simulation of the model is carried out using hypothetical parametric values to support the analytical results. From the numerical simulation, it is shown that the length of delay is inversely proportional to the parameter
$$A$$
which measures the level of interaction between prey and predator.
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