Global properties of a general predator-prey model with non-symmetric attack and consumption rate
The paper focuses on deriving conditions which ensure the global stability of a predator-prey (consumer-supplier) type of model under the assumption that the resource is partially wasted by the predator (consumer). The paper begins with a discussion about the study of population stability and oscillations. Unlike many previous studies, this paper considers more generally ecosystem-stability which is not based on a specific choice of functional response. The model under consideration, in which the consumption rate is not proportional to the attack rate, is introduced in section 2. The existence of a globally asymptotic stable equilibrium state under 13 given hypotheses is stated and proved in theorem 3.1. Global neutral stability and global asymptotic stability, both under weaker hypotheses, are proved in theorems 3.2 and 3.3. The author concludes that, in general, wastage increases the rate of convergence of solutions to the equilibrium state.
scientific article; zbMATH DE number 5827362