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- Title
Persistence, Turing Instability and Hopf Bifurcation in a Diffusive Plankton System with Delay and Quadratic Closure.
- Authors
Zhao, Jiantao; Wei, Junjie
- Abstract
A reaction-diffusion plankton system with delay and quadratic closure term is investigated to study the interactions between phytoplankton and zooplankton. Sufficient conditions independent of diffusion and delay are obtained for the persistence of the system. Our conclusions show that diffusion can induce Turing instability, delay can influence the stability of the positive equilibrium and induce Hopf bifurcations to occur. The computational formulas which determine the properties of bifurcating periodic solutions are given by calculating the normal form on the center manifold, and some numerical simulations are carried out for illustrating the theoretical results.
- Subjects
HOPF bifurcations; QUADRATIC equations; REACTION-diffusion equations; MATHEMATICAL formulas; MANIFOLDS (Mathematics)
- Publication
International Journal of Bifurcation & Chaos in Applied Sciences & Engineering, 2016, Vol 26, Issue 3, p-1
- ISSN
0218-1274
- Publication type
Article
- DOI
10.1142/S0218127416500474