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Dynamics of a predator-prey model with generalized Holling type functional response and mutual interference
Kwadwo Antwi-Fordjour1, Rana D Parshad2, Matthew A Beauregard3
1Department of Mathematics and Computer Science, Samford University, Birmingham, AL 35229, USA.
Mathematical Biosciences
|June 23, 2020
Summary
Mutual interference and prey refuge significantly impact predator-prey models. Introducing prey refuge can prevent population extinction, ensuring species persistence.
Area of Science:
- Theoretical Ecology
- Mathematical Biology
- Population Dynamics
Background:
- Predator-prey dynamics are influenced by mutual interference and prey refuge.
- The degree of mutual interference in predator-prey models is a subject of ongoing theoretical debate.
- A generalized Holling type functional response model is utilized, including non-smooth cases.
Purpose of the Study:
- To investigate the combined effects of the mutual interference exponent and prey refuge on predator-prey model behavior.
- To analyze the model's dynamical properties, including bifurcations and finite-time extinction.
- To determine conditions under which prey refuge promotes population persistence.
Main Methods:
- Mathematical modeling of predator-prey interactions with a generalized Holling type functional response.
- Analysis of dynamical systems to derive conditions for saddle-node, transcritical, and Hopf bifurcations.
- Derivation of conditions for finite-time prey extinction and persistence under refuge.
- Numerical simulations to validate analytical findings.
Main Results:
- Conditions for various bifurcations (saddle-node, transcritical, Hopf) were derived.
- A sufficient condition for finite-time extinction of the prey species was established.
- The introduction of prey refuge was shown to yield population persistence.
- Numerical simulations corroborated the analytical results.
Conclusions:
- The interplay between mutual interference and prey refuge critically shapes predator-prey dynamics.
- Finite-time extinction of predator and prey populations is possible, aligning with classical ecological observations.
- Prey refuge is a crucial factor for ensuring population persistence in these models.
Keywords:
Analytic guidelinesFinite time extinctionGeneralized interferenceHopf-bifurcationPrey refugeMore Related Videos
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