In this paper, a homogeneous diffusive plant–herbivore model with toxin-determined functional response subject to the homogeneous Neumann boundary condition in the one dimensional spatial open bounded domain is considered. By using Hopf bifurcation theorem and steady state bifurcation theorem due to Yi et al. (2009), we are able to show the existence of Hopf bifurcating periodic solutions (spatially homogeneous and non-homogeneous) and bifurcating non-constant steady state solutions. In particular, under certain conditions, the globally asymptotic stability of the positive constant steady state solutions and the non-existence of non-constant positive steady state solutions are investigated. These results allow the clear understanding of the mechanisms of the spatiotemporal pattern formations of this ecology model. In particular, our numerical results authenticate that toxicant parameter will play important roles in the stability and instability of the periodic solutions.

在本文中，考虑了在一维空间开放有界域中均质Neumann边界条件下具有毒素决定的功能性反应的均质扩散植物-草食动物模型。通过使用霍普夫分叉定理和稳态分叉定理，由于伊等人。（2009年），我们能够证明存在Hopf分岔周期解（空间齐次和非齐次）和分岔非恒定稳态解的存在。特别是，在一定条件下，研究了正恒定稳态解的全局渐近稳定性和非恒定正稳态解的不存在性。这些结果可以清楚地了解这种生态模型的时空格局形成的机制。尤其是，