Convergence of ecological competition between two species.

*(English)*Zbl 0725.92025We consider a two-species system in which the first species would fare better in the absence of the second and the second is dependent on the first as it is to survive. That is, we are dealing with two species host parasite systems in which the parasite depends for subsistence on a single species of host and can not turn to an alternative food source.

We give a method for the convergence of the solutions of the prey- predator competitive system with a set of sufficient conditions. The theory of ecological competition modelled by the system in this paper is neither specific about the resource of the prey competed for nor specific about how the prey acquire and utilize the resources.

We give a method for the convergence of the solutions of the prey- predator competitive system with a set of sufficient conditions. The theory of ecological competition modelled by the system in this paper is neither specific about the resource of the prey competed for nor specific about how the prey acquire and utilize the resources.

##### Keywords:

convergence of solutions; Lotka-Volterra equations; two species host parasite systems; prey-predator competitive system; ecological competition
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\textit{K. N. Murty} and \textit{M. A. S. Srinivas}, J. Math. Anal. Appl. 158, No. 2, 333--341 (1991; Zbl 0725.92025)

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##### References:

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