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Nonlinear Dynamics

, Volume 95, Issue 3, pp 1731–1745 | Cite as

Rich spatial–temporal dynamics in a diffusive population model for pioneer–climax species

  • Ying Su
  • Xingfu ZouEmail author
Original Paper
  • 246 Downloads

Abstract

A general diffusive population model for interactions of pioneer and climax species subject to the no-flux boundary condition is considered. Local and global steady-state bifurcations as well as Hopf bifurcations are investigated. A condition for Turing instability not to happen is obtained, and the conditions for occurrences of Turing bifurcations and Hopf bifurcations are also obtained. Numerical simulations are carried out to demonstrate and extend the obtained analytic results which suggest that the spatial diffusion may make the climax species more dominant. The results indicate that the model, with spatial diffusion incorporated , can have very rich spatial–temporal dynamics.

Keywords

Pioneer species Climax species Diffusion Hopf bifurcation Turing bifurcation Spatial–temporal pattern 

Mathematics Subject Classification

35B32 35K57 92B05 92D25 

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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Department of MathematicsHarbin Institute of TechnologyHarbinPeople’s Republic of China
  2. 2.Department of Applied MathematicsUniversity of Western OntarioLondonCanada

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