The dynamics of two diffusively coupled predator-prey populations

Area of Science:

• Ecology
• Mathematical Biology
• Population Dynamics

Background:

• Predator-prey models are fundamental to ecology.
• Metapopulation theory often assumes asynchronous local dynamics.
• Understanding spatial coupling effects is crucial for population regulation.

Purpose of the Study:

• To investigate the conditions leading to synchronous versus asynchronous dynamics in a two-patch predator-prey system.
• To analyze the impact of predator migration rates on population stability and behavior.
• To explore the emergence of complex dynamics like chaos in spatially structured populations.

Main Methods:

• A mathematical model of predator-prey dynamics in two coupled patches was developed.
• Prey exhibit logistic growth; predators show a Holling type II functional response.
• Predator migration between patches was incorporated, and bifurcation diagrams were used to analyze dynamics.

Main Results:

• Low predator migration rates synchronize population oscillations.
• Intermediate rates destabilize synchronous oscillations, leading to asynchronous dynamics, including periodic, quasi-periodic, and chaotic attractors.
• High migration rates can result in equilibria or limit cycles where one patch is devoid of prey.

Conclusions:

• Spatial predator-prey systems can exhibit complex dynamics driven by local interactions and migration.
• Contrary to intuition, low migration can lead to synchronization, while intermediate migration promotes desynchronization and chaos.
• The interplay between local population dynamics and migration is a key regulatory mechanism in spatial predator-prey systems.