We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Stability and bifurcation analysis in a diffusive predator–prey model with delay and spatial average.
- Authors
Song, Yongli; Shi, Qingyan
- Abstract
In this paper, we study the effect of spatial average and time delay on the dynamics of a diffusive predator–prey model under the Neumann boundary condition. Compared to the model without spatial average, the delay‐induced Hopf bifurcation at the first critical value of delay is nonhomogeneous due to the joint effects of spatial average and delay, and spatiotemporal patterns arise. Also, we show that the spatially homogeneous and nonhomogeneous periodic patterns may switch for different bifurcation parameter values. Moreover, a double Hopf bifurcation occurs at the intersection point of the homogeneous and nonhomogeneous Hopf bifurcation curves, and spatially nonhomogeneous quasi‐periodic patterns can be observed via numerical simulations near the double Hopf bifurcation point. The normal form algorithm for the spatially nonhomogeneous/homogeneous Hopf bifurcation is derived for a general reaction‐diffusion system with spatial average and delay.
- Subjects
BIFURCATION diagrams; HOPF bifurcations; NEUMANN boundary conditions; PREDATION; SPATIAL systems
- Publication
Mathematical Methods in the Applied Sciences, 2023, Vol 46, Issue 5, p5561
- ISSN
0170-4214
- Publication type
Article
- DOI
10.1002/mma.8853