Coexistence Steady States in a Predator-Prey Model
Christoph Walker (LUH)
TL;DR
This paper analyzes an age-structured predator-prey model with diffusion and nonlinear interactions, demonstrating bifurcation of coexistence steady states as predator or prey fertility varies.
Contribution
It establishes bifurcation results for positive coexistence steady states in a complex predator-prey system with age structure and nonlinearities.
Findings
Coexistence steady states bifurcate from marginal states as fertility varies.
Bifurcation occurs when predator fertility is the bifurcation parameter.
Similar bifurcation results are obtained when prey fertility varies.
Abstract
An age-structured predator-prey system with diffusion and Holling-Tanner-type nonlinearities is considered. Regarding the intensity of the fertility of the predator as bifurcation parameter, we prove that a branch of positive coexistence steady states bifurcates from the marginal steady state with no prey. A similar result is obtained when the fertility of the prey varies.
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Taxonomy
TopicsMathematical and Theoretical Epidemiology and Ecology Models · Mathematical Biology Tumor Growth · Evolution and Genetic Dynamics