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\begin{document}

\title{Global bifurcation and structure of stationary patterns of a diffusive
system of plant-herbivore interactions with toxin-determined functional
responses}



\author[1]{Cunbin An}%
\author[2]{Wei Han}%
\affil[1]{Shanxi Datong University}%
\affil[2]{North University of China}%


\vspace{-1em}



  
  \date{May 04, 2024}


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\begin{abstract}
In this paper, a homogeneous diffusive system of plant-herbivore
interactions with toxin-determined functional responses is considered.
We are mainly interested in studying the existence of global steady
state bifurcations of the diffusive system. In particular, we also
consider the case when the bifurcation parameter, one of the diffusion
rates, tends to infinity. The corresponding system is called shadow
system. By using time-mapping methods, we can show the existence of the
positive non-constant steady state solutions. The results tend to
describe the mechanism of the spatial pattern formations for this
particular system of plant-herbivore interactions.%
\end{abstract}%



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