Figure 8

Single mode pattern. Figure 8 gives the comparison among the numerical solution of system (1.3) (left), the weakly nonlinear first order approximation of the solution with stable equilibrium \((A_{1\infty},0)\) (medium) and the weakly nonlinear first order approximation of the solution with stable equilibrium \((0, A_{2\infty})\) (right) under double and non-resonant eigenvalue case. The parameters are \(r_{1}=0.6\), \(r_{2}=0.3\), \(c_{1}=c_{2}=0.1\), \(d_{1}=d_{2}=0.1\), \(\alpha_{21}=0.3\), \(a_{1}=0.1\), \(a_{2}=0.2\), \(\alpha_{12}=0.4\), \(\beta_{1}=0.2\). Here \(b^{c}=0.993\), \(\varepsilon=0.36\) and \(b=(1+\epsilon^{2})b^{c}\).