物种起源
发表于 2025-3-25 06:13:47
Reaction-Diffusion Equations on a Square, d ∈ R is the diffusion rate of the second substance. The functions .. : ...., . = 1,2, describe reactions among the substances. They are supposed to be sufficiently smooth and have a polynomial growth.for some constants .., .., . 0. Furthermore, we assume
ENNUI
发表于 2025-3-25 11:11:08
Steady/Steady State Mode Interactions,ple bifurcations induced by symmetries in the problem. More precisely, we treat multiple bifurcations as a special case of mode interactions since this kind of linear degeneracy occurs as a consequence of the geometric property of the problem.
施加
发表于 2025-3-25 15:03:28
Homotopy of Boundary Conditions,ions. Properties and spectrum of the Laplacian are decisive for analysis of dynamics and bifurcations of reaction-diffusion equations. As we have seen in previous chapters, linear stability of a solution .= .. is determined by eigenvalues of the linearized operator
放肆的你
发表于 2025-3-25 17:08:22
A Numerical Bifurcation Function for Homoclinic Orbits,cs near a homoclinic orbit reveals long time behavior of a system. It gives also hints on global bifurcations, namely bifurcation of homoclinic orbits. This is a complementary to the local bifurcations which we have studied with the Liapunov-Schmidt method and the center manifold theory.
单独
发表于 2025-3-25 22:24:45
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Indecisive
发表于 2025-3-26 02:42:27
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inveigh
发表于 2025-3-26 07:13:28
Continuation of Nonsingular Solutions,: ...... is a smooth mapping. The unknown . describes state of the system and A represents parameters. Typically, this equation can be considered as spatial discretized reaction-diffusions equations, stationary problem of well-stirred reactions, population model in biological systems. Variation of a
调色板
发表于 2025-3-26 11:27:19
Detecting and Computing Bifurcation Points,near problems of the form .where . : . x .. → . is a “smooth” mapping and λ ∈ .. represents various control parameters, e.g. Reynolds number, catalyst, temperature, density, initial or final products, etc. Bifurcation theory studies how solutions of (3.1) and their stability change as the parameter
meritorious
发表于 2025-3-26 14:50:27
Branch Switching at Simple Bifurcation Points,g solution curves to gain insight how one physical state transits to another as control parameter changes and how sensitive such a transition is with respect to the parameter. Often very interesting scenario occurs as the solution moves from one branch to another. Branch switching and path following
黄油没有
发表于 2025-3-26 17:10:36
Bifurcation Problems with Symmetry,lying symmetries, which origins, e.g., from the Euclidean symmetry of the Laplace operator. The continuous symmetry of a differential operator is often subjected to symmetries of domains, boundary conditions and reaction terms. We observe it normally in a discrete form. But its existence as underlyi