Abstract
In this paper we consider symmetric solutions of reaction–diffusion equations on an unbounded root-like metric graph. We first prove a version of the zero number diminishing properties on the graph, and then use them to show a convergence result for bounded and symmetric solution of general equations. As application, we provide a complete spreading-transition-vanishing trichotomy result on the asymptotic behaviour for solutions of the bistable reaction–diffusion equation on the graph.
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