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Allee effect-driven complexity in a spatiotemporal predator-prey system with fear factor.
Yuhong Huo1, Gourav Mandal2, Lakshmi Narayan Guin2
1School of Finance and Mathematics, Huainan Normal University, Dongshanxi Street, Huainan, 232038, China.
Mathematical Biosciences and Engineering : MBE
|December 5, 2023
Summary
This study introduces a spatiotemporal prey-predator model incorporating fear and Allee effects. The Allee effect significantly influences system dynamics, inducing complex bifurcations and pattern transitions in predator-prey interactions.
Area of Science:
- Mathematical Biology
- Ecology
- Dynamical Systems
Background:
- Predator-prey models are fundamental in ecology.
- Fear and Allee effects are crucial factors influencing population dynamics.
- Spatiotemporal dynamics can lead to complex ecological patterns.
Purpose of the Study:
- To develop and analyze a spatiotemporal prey-predator model with fear and Allee effects.
- To investigate the impact of these effects on stability and bifurcation phenomena.
- To explore pattern formation and transitions in ecological systems.
Main Methods:
- Establishing global existence of solutions.
- Analyzing conditions for non-negative spatially homogeneous equilibria.
- Studying stability and bifurcation analysis of equilibria.
- Utilizing numerical simulations to validate theoretical findings.
Main Results:
- The Allee effect and fear factor induce complex bifurcation scenarios.
- Large Allee effect drives Turing instability and pattern transitions.
- Small Allee effect can stabilize the system.
- The Allee effect can induce various codimension-one and codimension-two bifurcations.
- Pattern transitions from circular rings to coldspot and stripe patterns were observed.
Conclusions:
- The Allee effect plays a critical role in shaping the dynamics of spatiotemporal predator-prey systems.
- Fear and Allee effects can lead to rich and complex ecological pattern formation.
- Theoretical predictions are supported by numerical simulations, highlighting the model's validity.
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