Dynamics of the density dependent predator–prey system with Beddington–DeAngelis functional response
By Haiyin Li, Yasuhiro Takeuchi. 2011
181 citations recorded by the source corpus.
Abstract Two models of a density dependent predator–prey system with Beddington–DeAngelis functional response are systematically considered. One includes the time delay in the functional response and the other does not. The explorations involve the permanence, local asymptotic stability and global asymptotic stability of the positive equilibrium for the models by using stability theory of differential equations and Lyapunov functions. For the permanence, the density dependence for predators is shown to give some negative effect for the two models. Further the permanence implies the local asymptotic stability for a positive equilibrium point of the model without delay. Also the global asymptotic stability condition, which can be easily checked for the model is obtained. For the model with time delay, local and global asymptotic stability conditions are obtained.
Subfields: Genetics, Modeling and Simulation, Public Health, Environmental and Occupational Health
View Paper: https://www.semanticscholar.org/paper/7473c1c8e58bd1ef8ee08fa4d6a17f47688d3fbf
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Citations in the corpus
- Dynamical analysis of a prey–predator model with Beddington–DeAngelis type function response incorporating a prey refuge (2014, methodology): “Also in [21], an statistical evidence from nineteen prey–predator systems results that three predator-dependent functional responses (namely Beddington–DeAngelis, Crowley–Martin and Hassel– Varley) can provide better description of predator feeding over the range of prey–predator abundance [9].”