### Mathematical Biosciences and Engineering

2016, Issue 4: 857-885. doi: 10.3934/mbe.2016021

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

• Received: 01 August 2015 Accepted: 29 June 2018 Published: 01 May 2016
• MSC : Primary: 35J55, 35K57; Secondary: 92C15, 92C40.

• 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.

Citation: Jun Zhou. Bifurcation analysis of a diffusive plant-wrack model with tide effect on the wrack[J]. Mathematical Biosciences and Engineering, 2016, 13(4): 857-885. doi: 10.3934/mbe.2016021

### Related Papers:

• 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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