Figure 2

There exist some unstable spatially homogenous periodic solutions that are bifurcating from the positive equilibrium \((u^{*},v^{*} )\) of system (1.1) when the parameter \(c=0.75>0.7366\). Here we choose to set parameter values as \(d_{1}=0.05\), \(d_{2}=0.1\), \(\gamma =1\), \(\beta =0.5048\), and for the initial values we take \(u(x,0)=0.3042+0.05\cos x\), \(v(x,0)=0.3652+0.05\cos x\)