Stability and Hopf Bifurcation Analysis of a Gene Expression Model with Diffusion and Time Delay

Figure 2

Numerical simulations system (4) with 𝑑₁=0.002, 𝑑₂=0.02, 𝑏=𝑐=0.03, 𝑛=2, 𝑝₀=0.4, and 𝜏=30>𝜏⁰₀. The initial values are 𝑚₀(𝑥)=0.2+0.1cos𝑥; 𝑝₀(𝑥)=5.6−0.01cos𝑥. The positive equilibrium 𝐸^∗(0.1684,5.6134) of system (4) becomes unstable and there exist stable spatially homogeneous periodic solutions.