Develop a PDE-based model that describes the dynamics of a predator-prey ecosystem with the following assumptions:
Develop a PDE-based model that describes the dynamics of a predator-prey ecosystem with the following assumptions:
• The prey population grows following the logistic growth model.
• The predator population tends to decay naturally without prey.
• Predation (i.e., encounter of prey and predator populations) increases the predator population while it decreases the prey population.
• The predator population tends to move toward areas with high prey density.
• The prey population tends to move away from areas with high predator density.
• Both populations diffuse over space.
SAMPLE ASSIGNMENT
