Dynamical Analysis of a Delayed Reaction-Diffusion Predator-Prey System

Figure 2

The solution of system (1.7) tends to the positive equilibrium 𝐸^∗. The parameters are taken as 𝛼=2, 𝛽=0.2, 𝛾=0.5, 𝑏=2, 𝑐=3, 𝑚=1, 𝑑₁=0.01, 𝑑₂=0.1, 𝜏=0.9, and the initial values 𝑢(𝑥,𝑡)=0.662+0.01𝑡cos𝑥, 𝑣(𝑥,𝑡)=1.649+0.01𝑡sin𝑥, 𝑡∈[−0.9,0], 𝑥∈[0,𝜋]. In this case, 𝜏<𝜏⁰₀=1.0289.

(a)

(b)