Predator–prey model with prey-taxis and diffusion

The objective of this paper is to investigate the effect of prey-taxis on predator–prey models with Paramecium aurelia as the prey and Didinium nasutum as its predator. The logistic Lotka–Volterra predator–prey models with prey-taxis are solved numerically with four different response functions, two initial conditions and one data set. Routh–Hurwitz’s stability conditions are used to obtain the bifurcation values of the taxis coefficients for each model. We show that both response functions and initial conditions play important roles in the pattern formation. When the value of the taxis coefficient becomes considerably higher than the bifurcation value, chaotic dynamics develop. As diffusion in predator velocity is incorporated into the system, the system returns to a cyclic pattern.