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In this paper we consider one-predator-two-prey population dynamics described by a control system. We study and compare conditions for permanence of the system for three types of predator feeding behaviors: (i) specialized feeding on the more profitable prey type, (ii) generalized feeding on both prey types, and (iii) optimal foraging behavior. We show that(More)
In this paper we discuss uniform persistence (UP) criteria of two prey- one predator systems, where we consider that the predator's diet selection is a sigmoidal function of the most profitable prey type in place of a step function of conventional diet choice theory. We also derive UP results of the system with direct interspecific competition between the(More)
This paper considers a Lotka-Volterra type of model of competition between a commensal pair of species and a mutualistic pair, presumed to have descended from a single ancestral pair of species. The species are behaviourally isolated but compete for resources. We have studied in detail the effects of the benefits of mutualism over commensalism.(More)
Considering a model of a generalized Gause-type four-species system of two predator-prey pairs linked by competition, the authors derive sufficient conditions for the existence of three different invariant cyclic sets connecting saddle points and limit cycle(s) on the boundary of its state space. Also discussed is the uniform persistence of the model in the(More)
We consider a four-species model based on competition and show that the whole four-species system collapses to a definite single species equilibrium at its carrying capacity. To do so, we use the results of Hirsch, Van Den Driessche and Zeeman, Hofbauer and Sigmund, and the product theorem of the Conley connection matrix theory by Mischaikow and Reineck.
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