Mathematical Biosciences and Engineering, 2016, 13(4): 857-885. doi: 10.3934/mbe.2016021

Primary: 35J55, 35K57; Secondary: 92C15, 92C40.

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Bifurcation analysis of a diffusive plant-wrack model with tide effect on the wrack

1. School of Mathematics and Statistics, Southwest University, Chongqing, 400715

This paper deals with the spatial, temporal and spatiotemporal dynamics of a spatial plant-wrack model. The parameter regions for the stability and instability of the unique positive constant steady state solution are derived, and the existence of time-periodic orbits and non-constant steady state solutions are proved by bifurcation method. The nonexistence of positive nonconstant steady state solutions are studied by energy method and Implicit Function Theorem. Numerical simulations are presented to verify and illustrate the theoretical results.
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