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adsorbate-induced phase transition model I: Existence
Global properties of a general predator-prey model with non-symmetric attack and consumption rate
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.