Double Hopf bifurcation in nonlocal reaction-diffusion systems with spatial average kernel
Zuolin Shen, Yang Liu, Junjie Wei
Abstract
In this paper, we consider a general reaction-diffusion system with nonlocal effects and Neumann boundary conditions, where a spatial average kernel is chosen to be the nonlocal kernel. By virtue of the center manifold reduction technique and normal form theory, we present a new algorithm for computing normal forms associated with the codimension-two double Hopf bifurcation. The theoretical results are applied to a predator-prey model, and complex dynamic behaviors such as spatially nonhomogeneous periodic oscillations and spatially nonhomogeneous quasi-periodic oscillations could occur.
Topics & Concepts
Center manifoldKernel (algebra)MathematicsReaction–diffusion systemHopf bifurcationNeumann boundary conditionMathematical analysisCodimensionSaddle-node bifurcationBoundary (topology)BifurcationPure mathematicsPhysicsNonlinear systemQuantum mechanicsMathematical and Theoretical Epidemiology and Ecology ModelsDifferential Equations and Numerical MethodsAdvanced Mathematical Modeling in Engineering