Bifurcation theory and applications wang shouhong ma tian
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With this new notion of bifurcation, many longstanding bifurcation problems in science and engineering are becoming accessible, and are treated in the second part of the book. In this note, we present a fast communication of a new bifurcation theory for nonlinear evolution equations, and its application to Rayleigh-BĂ©nard Convection. Existence theory and strong attractors for the Rayleigh-BĂ©nard problem with a large aspect ratio. . Structural stability of rate-independent nonpotential flows. Structural stability in a minimization problem and applications to conductivity imaging. The applications provide, on the one hand, general recipes for other applications of the theory addressed in this book, and on the other, full classifications of the bifurcated attractor and the global attractor as the control parameters cross certain critical values, dictated usually by the eigenvalues of the linearized problems.

A weak attractor and properties of solutions for the three-dimensional BĂ©nard problem. Global Asymptotic Stability and Hopf Bifurcation for a Blood Cell Production Model. This theory includes the following three aspects. With this new notion of bifurcation, many longstanding bifurcation problems in science and engineering are becoming accessible, and are treated in the second part of the book. Weak structural stability of pseudo-monotone equations.

On the central stability zone for linear discrete-time Hamiltonian systems. Admissibility, a general type of Lipschitz shadowing and structural stability. The book first introduces bifurcation theories recently developed by the authors, on steady state bifurcation for a class of nonlinear problems with even order nondegenerate nonlinearities, regardless of the multiplicity of the eigenvalues, and on attractor bifurcations for nonlinear evolution equations, a new notion of bifurcation. Structural stability for the splash singularities of the water waves problem. In addition, the technical method developed provides a recipe, which can be used for many other problems related to bifurcation and pattern formation. Structural stability of optimal control problems.

The proofs of the main theorems presented will appear elsewhere. The bifurcation theory is based on a new notion of bifurcation, called attractor bifurcation. Series Title: , Series A,, Monographs and treatises ;, v. Stability of equilibria points for a dumbbell satellite when the central body is oblate spheroid. The applications provide, on the one hand, general recipes for other applications of the theory addressed in this book, and on the other, full classifications of the bifurcated attractor and the global attractor as the control parameters cross certain critical values, dictated usually by the eigenvalues of the linearized problems. It is expected that the book will greatly advance the study of nonlinear dynamics for many problems in science and engineering. Contents: Introduction to steady state bifurcation theory -- Introduction to dynamic bifurcation -- Reduction procedures and stability -- Steady state bifurcations -- Dynamic bifurcation theory: Finite dimensional case -- Dynamic bifurcation theory: Infinite dimensional case -- Bifurcations for nonlinear elliptic equations -- Reaction-diffusion equations -- Pattern formation and wave equations -- Fluid dynamics.

Responsibility: Tian Ma, Shouhong Wang. It is expected that the book will greatly advance the study of nonlinear dynamics for many problems in science and engineering. Second, the bifurcated attractor A R is asymptotically stable. Conference Publications, 2003, 2003 Special : 734-741. The book first introduces bifurcation theories recently developed by the authors, on steady state bifurcation for a class of nonlinear problems with even order nondegenerate nonlinearities, regardless of the multiplicity of the eigenvalues, and on attractor bifurcations for nonlinear evolution equations, a new notion of bifurcation. The book first introduces bifurcation theories recently developed by the authors, on steady state bifurcation for a class of nonlinear problems with even order nondegenerate nonlinearities, regardless of the multiplicity of the eigenvalues, and on attractor bifurcations for nonlinear evolution equations, a new notion of bifurcation. We study in this article the bifurcation and stability of the solutions of the Boussinesq equations, and the onset of the Rayleigh-Benard convection.

Existence and dimension of the attractor for the BĂ©nard problem on channel-like domains. First, the problem bifurcates from the trivial solution an attractor A R when the Rayleigh number R crosses the first critical Rayleigh number R c for all physically sound boundary conditions, regardless of the multiplicity of the eigenvalue R c for the linear problem. Asymptotic stability of traveling wavefronts in a delayed population model with stage structure on a two-dimensional spatial lattice. The applications provide, on the one hand, general recipes for other applications of the theory addressed in this book, and on the other, full classifications of the bifurcated attractor and the global attractor as the control parameters cross certain critical values, dictated usually by the eigenvalues of the linearized problems. The book first introduces bifurcation theories recently developed by the authors, on steady state bifurcation for a class of nonlinear problems with even order nondegenerate nonlinearities, regardless of the multiplicity of the eigenvalues, and on attractor bifurcations for nonlinear evolution equations, a new notion of bifurcation. With this new notion of bifurcation, many longstanding bifurcation problems in science and engineering are becoming accessible, and are treated in the second part of the book.

Based on this new bifurcation theory, we obtain a nonlinear theory for bifurcation and stability of the solutions of the Boussinesq equations, and the onset of the Rayleigh-BĂ©nard convection. Positive feedback control of Rayleigh-BĂ©nard convection. Introduction to Steady State Bifurcation Theory Introduction to Dynamic Bifurcation Reduction Procedures and Stability Steady State Bifurcation Dynamic Bifurcation Theory: Finite Dimensional Case Dynamic Bifurcation Theory: Infinite Dimensional Case Bifurcations for Nonlinear Elliptic Equations Reaction-Diffusion Equations Pattern Formation and Wave Equations Fluid Dynamics. In particular, this book covers the Kuramoto-Sivashinsky equation, the Cahn-Hillard equation, the Ginzburg-Landau equation, reaction-diffusion equations in biology and chemistry, and more. The book first introduces bifurcation theories recently developed by the authors, on steady state bifurcation for a class of nonlinear problems with even order nondegenerate nonlinearities, regardless of the multiplicity of the eigenvalues, and on attractor bifurcations for nonlinear evolution equations, a new notion of bifurcation. It is expected that the book will greatly advance the study of nonlinear dynamics for many problems in science and engineering.

Bifurcation and stability of two-dimensional double-diffusive convection. Dynamic bifurcation theory of Rayleigh-BĂ©nard convection with infinite Prandtl number. Bifurcation analysis to Rayleigh-BĂ©nard convection in finite box with up-down symmetry. Third, when the spatial dimension is two, the bifurcated solutions are also structurally stable and are classified as well. The E-mail message field is required.

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