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October  2010, 14(3): 1095-1103. doi: 10.3934/dcdsb.2010.14.1095

Global properties of a general predator-prey model with non-symmetric attack and consumption rate

Andrei Korobeinikov 1,

1. 

MACSI, Department of Mathematics and Statistics, University of Limerick, Limerick

Received  October 2009 Revised  December 2009 Published  July 2010

Identification of conditions for stable coexistence of interacting populations is a problem of the highest priority in mathematical biology. This problem is usually considered under specific assumptions made regarding the functional forms of non-linear feedbacks. Apparently, such an approach is lacking generality. In this paper, we consider the dynamics of two species with interaction of predator--prey (consumer-supplier) type with the assumption that a part of the resource is neglected or wasted by the predator (consumer). This model describes, for instance, killing for fun; such behaviour is typical for many predators when the prey is abundant.
   We assume that the functional responses that are usually included in such models are given by unspecified functions. Using the direct Lyapunov method, we derive the conditions which ensure global asymptotic stability of this model. It is remarkable that these conditions impose much weaker constraints on the system properties than that are usually assumed.
Keywords: direct Lyapunov method, Ecosystem, mass action, compartment model, endemic equilibrium state, prey-predator model, Lyapunov function, consumer-supplier model, Lotka-Volterra model, global stability, non-linear incidence rate, coexistence, infectious disease, wastage., non-linear attack rate.
Mathematics Subject Classification: Primary: 592D30; Secondary: 34D2.
Citation: Andrei Korobeinikov. Global properties of a general predator-prey model with non-symmetric attack and consumption rate. Discrete & Continuous Dynamical Systems - B, 2010, 14 (3) : 1095-1103. doi: 10.3934/dcdsb.2010.14.1095
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