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Influence of Allee effect on the spatiotemporal behavior of a diffusive predator-prey model with Crowley-Martin type
Lakshmi Narayan Guin1, Pallav Jyoti Pal2, Jawaher Alzahrani3
1Department of Mathematics, Visva-Bharati, Santiniketan, West Bengal, 731235, India.
This study explores a predator-prey model with an Allee effect on prey and a Crowley-Martin response. It reveals complex dynamics, including bi-stability and pattern formation, influenced by both the Allee effect and diffusion.
Area of Science:
- Ecology
- Mathematical Biology
- Population Dynamics
Background:
- Predator-prey models are crucial for understanding ecological interactions.
- The Allee effect significantly impacts population growth dynamics.
- Crowley-Martin functional response describes predator feeding behavior.
Purpose of the Study:
- To analyze a predator-prey model incorporating the Allee effect for prey and a Crowley-Martin response for predators.
- To investigate the stability and bifurcation properties of the proposed model.
- To explore the spatial dynamics and pattern formation in a reaction-diffusion version of the model.
Main Methods:
- Mathematical modeling of predator-prey interactions.
- Stability analysis and bifurcation theory.
- Numerical simulations for spatiotemporal dynamics.
Main Results:
- The model exhibits bi-stability and the existence of a separatrix.
- The Allee effect and diffusion drive pattern formation, including hot spots, stripes, and labyrinthine structures.
- Numerical simulations validate the theoretical findings of the spatiotemporal model.
Conclusions:
- The Allee effect introduces significant complexity into predator-prey dynamics.
- Spatial diffusion plays a key role in generating diverse spatial patterns.
- The study provides insights into ecological pattern formation driven by population effects and spatial processes.
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