Dynamical analysis arising from the Willamowski-Rossler model

We study a three-dimensional Willamowski-Rossler model that is described as a spatially confined reaction system. To better restrict the parameter space of the chaotic dynamics of the system, the dynamics of boundary equilibria and subsystems of this model are investigated. According to the categories of the parameters, we classify two cases to discuss the relevant dynamics. For the extinction of this model, we obtain not only the local stability of the solutions but also global asymptotic stability. Furthermore, some amenable sufficient conditions for the uniform persistence for the model are given. Moreover, our analytic transversality conditions on the existence of periodic solutions via Hopf bifurcation are constructed, which is helpful to provide some theoretical analysis for exploring the parameter regions for the chaotic dynamics of the Willamowski-Rossler model. (C) 2022 Elsevier Inc. All rights reserved.