Titlebook: Numerical Bifurcation Analysis for Reaction-Diffusion Equations; Zhen Mei Book 2000 Springer-Verlag Berlin Heidelberg 2000 Numerics.Numeri

MAG

Liapunov-Schmidt Method,gebraic equations. This system is responsible for the bifurcation scenario and normally is easy to analyze. Another advantage of this approach is that the established singularity theory can be utilized directly to determine normal forms of these algebraic equations and their bifurcation scenario, se

衰老

Center Manifold Theory,anifold theory is used to reduce a dynamical system near a nonhyperbolic equilibrium or a periodic solution to a low-dimensional system with the vector field as functions of the critical modes. Furthermore, stability of solutions and local dynamics of the system can be derived from the low-dimension

Range-Of-Motion

Bone-Scan

One-Dimensional Reaction-Diffusion Equations, To ensure a correct reflection of bifurcation scenario in discretizations and to reduce imperfection of singularities, we consider a preservation of multiplicities of the bifurcation points in the discrete problems. A continuation-Arnoldi algorithm is exploited to trace the solution branches and to

結(jié)果

Reaction-Diffusion Equations on a Square,ndary conditions.Here . :— (....). are state variables representing concentrations of immediate products; λ ∈ .. is a vector of control parameters and d ∈ R is the diffusion rate of the second substance. The functions .. : ...., . = 1,2, describe reactions among the substances. They are supposed to

depreciate

Incorruptible

Steady/Steady State Mode Interactions,impose the homogeneous Dirichlet boundary conditions to these equations. We distinguish mode interactions resulted from multiple parameters from multiple bifurcations induced by symmetries in the problem. More precisely, we treat multiple bifurcations as a special case of mode interactions since thi

粘連

Homotopy of Boundary Conditions, is described by the Laplace operator ., as in the equation .for unstirred reactions. Diffusion is the underlying mechanism for spatial pattern formations. Properties and spectrum of the Laplacian are decisive for analysis of dynamics and bifurcations of reaction-diffusion equations. As we have seen

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