Topic

# Bifurcation diagram

About: Bifurcation diagram is a(n) research topic. Over the lifetime, 8379 publication(s) have been published within this topic receiving 139664 citation(s).

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01 Jan 1981

TL;DR: The Hopf Bifurcation Theorum has been used in many applications, such as Differential Difference and Integro-differential Equations (by hand).

Abstract: 1. The Hopf Bifurcation Theorum 2. Applications: Ordinary Differential Equations (by hand) 3. Numerical Evaluation of Hopf Bifurcation Formulae 4. Applications: Differential-Difference and Integro-differential Equations (by hand) 5. Applications: Partial Differential Equations (by hand).

2,025 citations

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12 Nov 2011

TL;DR: In this paper, the static and dynamic aspects of bifurcation theory, which are of particular pertinence to differential equations, have been discussed, and a discussion of the changes that occur in the structure of the set of zeros of a function as parameters in the function are varied.

Abstract: Having presented background material from functional analysis and the qualitative theory of differential equations, this text focuses on the static and dynamic aspects of bifurcation theory, which are of particular pertinence to differential equations. Static bifurcation theory is concerned with the changes that occur in the structure of the set of zeros of a function as parameters in the function are varied. Dynamic bifurcation theory is concerned with the changes that occur in the structure of the limit sets of solutions of differential equations as parameters in the vector field are varied.

1,777 citations

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01 Jan 1980

TL;DR: Asymptotic solutions of evolution problems bifurcation and stability of steady solution of evolution equations in one dimension imperfection theory and isolated solutions which perturb bifurbcation stability of stable solutions in two dimensions and n dimensions appendices as discussed by the authors.

Abstract: Asymptotic solutions of evolution problems bifurcation and stability of steady solutions of evolution equations in one dimension imperfection theory and isolated solutions which perturb bifurcation stability of steady solutions of evolution equations in two dimensions and n dimensions appendices - bifurcation of steady solution in two dimensions and the stability of the bifurcating solutions appendix - methods of projection for general problems of bifurcation into steady solutions bifurcation of periodic solutions from steady ones (Hopf Bifurcation) in two dimensions bifurcation of periodic solutions in the general case subharmonic bifurcation of forced T-periodic solutions subharmonic bifurcation of forced T-periodic solutions into asymptotically quasi-periodic solutions appendix - secondary subharmonic and symptotically quasi-periodic bifurcation of periodic solutions (of Hopf's type) in the autonomous case stability and bifurcation in conservative systems.

1,165 citations

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TL;DR: In this article, a simple homotopy is constructed by the modified Lindstedt-Poincare method, by the solution and the coefficient of linear term are expanded into series of the embedding parameter.

Abstract: A simple homotopy is constructed, by the modified Lindstedt-Poincare method(He,J.H. International Journal of Non-Linear Mechanics , 37, 2002, 309-314 ), the solution and the coefficient of linear term are expanded into series of the embedding parameter. Only one iteration leads to accurate solution.

871 citations

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01 Feb 1988

TL;DR: The from equilibrium to chaos practical bifurcation and stability analysis is genial in our digital library as discussed by the authors, an online admission to it is set as public so you can download it instantly.

Abstract: Rather than enjoying a good PDF next a cup of coffee in the afternoon, instead they juggled in the same way as some harmful virus inside their computer. from equilibrium to chaos practical bifurcation and stability analysis is genial in our digital library an online admission to it is set as public so you can download it instantly. Our digital library saves in multipart countries, allowing you to get the most less latency epoch to download any of our books past this one. Merely said, the from equilibrium to chaos practical bifurcation and stability analysis is universally compatible afterward any devices to read.

778 citations