A reaction-diffusion predator-prey model with pursuit, evasion, and nonlocal sensing

Area of Science:

• Mathematical Biology
• Ecology
• Partial Differential Equations

Background:

• Predator-prey models are crucial for understanding ecological dynamics.
• Nonlocal interactions and taxis significantly influence population distributions.
• Reaction-diffusion systems offer a framework for modeling spatial population dynamics.

Purpose of the Study:

• To propose and analyze a novel reaction-diffusion model for predator-prey interactions.
• To incorporate prey and predator taxis mediated by nonlocal sensing.
• To investigate the mathematical properties and dynamical behavior of the proposed model.

Main Methods:

• Developing a system of coupled parabolic and elliptic partial differential equations.
• Utilizing uniform estimates in Lebesgue spaces for theoretical analysis.
• Conducting numerical experiments to explore solution dynamics.

Main Results:

• Establishing boundedness and global well-posedness of the reaction-diffusion system.
• Demonstrating the influence of nonlocal sensing on population dynamics.
• Presenting numerical evidence of complex spatio-temporal patterns.

Conclusions:

• The proposed model provides a robust framework for studying predator-prey interactions with nonlocal sensing.
• Mathematical analysis confirms the stability and well-posedness of the system.
• Numerical simulations highlight the rich dynamical behaviors arising from taxis and nonlocal detection.