Existence and stability of periodic solutions for a delayed prey-predator model with diffusion effects

Hongwei Liang, Jia-Fang Zhang, Zhiping Zhang
2015 Electronic Journal of Qualitative Theory of Differential Equations  
Existence and stability of spatially periodic solutions for a delay preypredator diffusion system are concerned in this work. We obtain that the system can generate the spatially nonhomogeneous periodic solutions when the diffusive rates are suitably small. This result demonstrates that the diffusion plays an important role in deriving the complex spatiotemporal dynamics. Meanwhile, the stability of the spatially periodic solutions is also studied. Finally, in order to verify our theoretical
more » ... our theoretical results, some numerical simulations are also included.
doi:10.14232/ejqtde.2015.1.99 fatcat:vdbywboqgrd7rh7dpqmj3ix7cq