Invasion analysis on a predator-prey system in open advective environments

Area of Science:

• Ecology
• Mathematical Biology
• Environmental Science

Background:

• Predator-prey interactions are fundamental ecological processes.
• Advective environments, like rivers, introduce complex dynamics not seen in static systems.
• Understanding these dynamics is crucial for ecosystem management.

Purpose of the Study:

• To analyze a reaction-diffusion-advection system modeling predator-prey interactions in flowing environments.
• To identify critical parameters influencing population dynamics and stability.
• To investigate the conditions for predator invasion and coexistence.

Main Methods:

• Mathematical modeling using a reaction-diffusion-advection system.
• Application of global bifurcation theory.
• Analysis of critical mortality and advection rates.
• Numerical simulations to explore diffusion effects.

Main Results:

• Identified critical parameters (predator mortality, advection rates) that define system behavior.
• Established conditions for three scenarios: extinction, prey survival, or predator-prey coexistence.
• Proved the existence and uniqueness of coexistence steady states.
• Demonstrated that diffusion promotes predator invasion.

Conclusions:

• Advection significantly complicates predator-prey dynamics compared to non-advective systems.
• Predator invasion and stable coexistence are possible under specific, low mortality and advection conditions.
• Diffusion enhances predator success, favoring coexistence in riverine ecosystems.