Diffusion and distributed delay effects in a predator–prey system: A mathematical analysis

Abstract

This study explores a nonautonomous model of prey-predator dynamics, featuring continuous distributed delay and diffusion, with time-dependent parameters. Our model depicts two ecological patches hosting two species: predators remain localized in one patch, while prey can disperse between both. Our analysis concentrates on ensuring the model’s consistent presence and achieving global stability. Additionally, we derive necessary conditions for periodic solutions by developing a pertinent Lyapunov function.

Keywords

• Prey–predator
• Boundedness
• Stability
• Continuous distributed delay
• Periodic function
• Lyapunov functions