Figure 12

Double and resonant eigenvalue case with the stable state \(\pmb{H_{1}^{+}=(2.2682,-0.0559)}\) . In Figure 12, the parameters are \(r_{1}=0.6\), \(r_{2}=0.3\), \(c_{1}=c_{2}=0.1\), \(d_{1}=d_{2}=0.1\), \(\alpha_{12}=0.6\), \(\beta_{1}=0.25\), \(\alpha_{21}=0.3\), \(a_{1}=0.1\), \(a_{2}=0.1\). Here \(b^{c}=1.0769\), \(\varepsilon=0.15\) and \(b=1.2627\). The rectangular domain is chosen the same as in Figure 11. We give the comparison between the numerical solution of system (1.3) (left) and the weakly nonlinear first order approximation of the solution (right) with the stable state \(H_{1}^{+}=(2.2682, -0.0559)\) in the double and resonant eigenvalue case.