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Biological applications of bifurcation theory

About: Biological applications of bifurcation theory is a research topic. Over the lifetime, 2454 publications have been published within this topic receiving 55784 citations.


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Book
01 Jan 1995
TL;DR: One-Parameter Bifurcations of Equilibria in continuous-time systems and fixed points in Discrete-Time Dynamical Systems have been studied in this paper, where they have been used for topological equivalence and structural stability of dynamical systems.
Abstract: Introduction to Dynamical Systems * Topological Equivalence, Bifurcations, and Structural Stability of Dynamical Systems * One-Parameter Bifurcations of Equilibria in Continuous-Time Systems * One-Parameter Bifurcations of Fixed Points in Discrete-Time Systems * Bifurcations of Equilibria and Periodic Orbits in n-Dimensional Systems * Bifurcations of Orbits Homoclinic and Heteroclinic to Hyperbolic Equilibria * Other One-Parameter Bifurcations in Continuous-Time Systems * Two-Parameter Bifurcations of Equilibria in Continuous-Time Dynamical Systems * Two-Parameter Bifurcations of Fixed Points in Discrete-Time Dynamical Systems * Numerical Analysis of Bifurcations * A: Basic Notions from Algebra, Analysis, and Geometry * References * Index.

5,062 citations

Book
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).

2,090 citations

Book
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.

1,848 citations

Book
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.

779 citations

Book
01 Nov 1994
TL;DR: In this paper, Glendinning aims to equip the student with the mathematical know-how needed to appreciate stability theory and bifurcations, by providing an introduction to nonlinear differential equations.
Abstract: By providing an introduction to nonlinear differential equations, Dr Glendinning aims to equip the student with the mathematical know-how needed to appreciate stability theory and bifurcations. His approach is readable and covers material both old and new to undergraduate courses. Included are treatments of the Poincare-Bendixson theorem, the Hopf bifurcation and chaotic systems. The unique treatment that is found in this book will prove to be an essential guide to stability and chaos.

663 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202344
2022115
20211
20202
20193
201815