Hopf Bifurcation for Semilinear FDEs in General Banach Spaces
Shangzhi Li, Shangjiang Guo
Abstract
In this paper, we extend the equivariant Hopf bifurcation theory for semilinear functional differential equations in general Banach spaces and then apply it to reaction–diffusion models with delay effect and homogeneous Dirichlet boundary condition on a general open domain with a smooth boundary. In the process we derive the criteria for the existence and directions of branches of bifurcating periodic solutions, avoiding the process of center manifold reduction.
Topics & Concepts
MathematicsEquivariant mapCenter manifoldBanach spaceMathematical analysisHopf bifurcationNeumann boundary conditionDirichlet boundary conditionBoundary (topology)Pure mathematicsBifurcationNonlinear systemPhysicsQuantum mechanicsDifferential Equations and Numerical MethodsNumerical methods for differential equationsNonlinear Differential Equations Analysis