We consider a reaction–diffusion–ODE quiescent model in which the species can switch between mobile and immobile categories. We assume that the population inhabits a bounded region and study how its dynamics depend on the parameters describing switching rates and local population dynamics. Our results suggest that the transfer displays a stabilizing effect and inhibits the generation of spatial periodic solutions. A new method to obtain global stability and dissipative structure is also explored by constructing Lyapunov functionals to overcome the loss of compactness.

中文翻译：

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静态的反应扩散-ODE系统的动力学

我们考虑一个反应-扩散-ODE静态模型，其中物种可以在移动和不移动类别之间切换。我们假设人口居住在边界区域，并研究其动态如何取决于描述转换率和局部人口动态的参数。我们的结果表明，转移显示出稳定作用并抑制了空间周期解的产生。还通过构造Lyapunov官能团来探索一种获得整体稳定性和耗散结构的新方法，以克服紧密度的损失。