| Abstract: |
| We studied the Klausmeier-Gray-Scott model with non-diffusive plants, which is a coupled ODE-PDE system. We first established the critical conditions for instability of the constant steady state in general coupled ODE-PDE activator-inhibitor systems. In addition, the local structure of the nonconstant steady state and the condition to determine the local bifurcation direction were obtained. Secondly, for the model with non-diffusive plants, the Turing bifurcation was subcritical and the nonconstant steady-state bifurcation solutions were unstable. Finally, we investigated the spatial pattern of the model with slowly diffusive plants to understand the formation of the spike pattern of the model with non-diffusive plants. |
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