Open AccessBifurcation analysis of a diffusive plant-wrack model with tide effect on the wrack
Author(s) -
Jun Zhou
Publication year - 2016
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2016021
Subject(s) - constant (computer programming) , bifurcation , steady state (chemistry) , instability , stability (learning theory) , control theory (sociology) , function (biology) , time constant , mathematics , mechanics , physics , environmental science , computer science , nonlinear system , engineering , biology , chemistry , control (management) , quantum mechanics , machine learning , artificial intelligence , evolutionary biology , electrical engineering , programming language
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.