Skip to main content
Figure 11 | Boundary Value Problems

Figure 11

From: Cross-diffusion-driven Turing instability and weakly nonlinear analysis of Turing patterns in a uni-directional consumer-resource system

Figure 11

Double and resonant eigenvalue case with the only stable state \(\pmb{R^{+}=(0,1.9391)}\) . In Figure 11, the parameters are chosen as \(r_{1}=0.6\ r_{2}=0.3\), \(c_{1}=c_{2}=0.1\), \(d_{1}=d_{2}=0.1\), \(\alpha_{12}=0.5\), \(\beta_{1}=0.2\), \(\alpha_{21}=0.3\), \(a_{1}=0.1\), \(a_{2}=0.2\). Here \(b^{c}=0.9947\), \(\varepsilon=0.03\) and \(b=1.0254\). 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 only stable state \(R^{+}=(0, 1.9391)\) under double and resonant eigenvalue case. The spatial domain is confined to a rectangular domain with \(L_{x}=8\sqrt{3}\pi\) and \(L_{y}=4\pi\).

Back to article page