Permanence and Stability of a Stage-Structured Predator–Prey Model
By Wendi Wang, Giuseppe Mulone, F. Salemi, V. Salone. 2001
130 citations recorded by the source corpus.
Abstract A predator–prey model with a stage structure for the predator which improves the assumption that each individual predator has the same ability to capture prey is proposed. It is assumed that immature individuals and mature individuals of the predator are divided by a fixed age and that immature predators do not have the ability to attack prey. We obtain conditions that determine the permanence of the populations and the extinction of the populations. Furthermore, we establish necessary and sufficient conditions for the local stability of the positive equilibrium of the model. By exploiting the monotonicity of one equation of the model, we obtain conditions for the global attractivity of the positive equilibrium, which allow for long delay as long as the predator birth rate is large or the death rate of immature predators is small. By constructing Liapunov functionals, we also obtain conditions under which the positive equilibrium is globally stable when the delay is small.
Subfields: Genetics, Modeling and Simulation, Public Health, Environmental and Occupational Health
View Paper: https://www.semanticscholar.org/paper/c4e5a3ad0f8aeec22d03a31976afae10a7955410
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In Genetics
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Citations in the corpus
- Multiple periodic solutions of a delayed stage-structured predator–prey model with non-monotone functional responses (2007, methodology): “Sufficient conditions were obtained in [37] for the permanence and global stability of a positive equilibrium of the proposed model.”
- Permanence and global attractivity of stage-structured predator-prey model with continuous harvesting on predator and impulsive stocking on prey (2008, background): “Wang [ 16 ] studied the global analysis of the model by introducing the”