1 edition of Stability and Bifurcation Theory for Non-Autonomous Differential Equations found in the catalog.
|Statement||by Anna Capietto, Peter Kloeden, Jean Mawhin, Sylvia Novo, Rafael Ortega|
|Series||Lecture Notes in Mathematics -- 2065|
|Contributions||Kloeden, Peter, Mawhin, Jean, Novo, Sylvia, Ortega, Rafael, SpringerLink (Online service)|
|The Physical Object|
|Format||[electronic resource] :|
|Pagination||IX, 303 p. 26 illus., 9 illus. in color.|
|Number of Pages||303|
In au-tonomous ordinary differential equations this theory is well developed. As in the autonomous systems, non-autonomous bifurcation is understood as a qualitative change in the structure and stability of the invariant sets of the system. The purpose of the present chapter is once again to show on concrete new examples that chaos in one-dimensional unimodal mappings, dynamical chaos in systems of ordinary differential equations, diffusion chaos in systems of the equations with partial derivatives and chaos in Hamiltonian and conservative systems are generated by cascades of bifurcations under universal bifurcation .
Equilibrium Solutions and Stability of Differential Equations (Differential Equations 36) Bifurcation diagrams - Duration: Euler's Method Differential Equations, Examples. Although, bifurcation theory of ordinary differential equations with autonomous and periodic time dependence is a major object of research in the study of dynamical systems since decades, the.
examples from areas where the theory may be applied. As diﬀerential equations are equations which involve functions and their derivatives as unknowns, we shall adopt throughout the view that diﬀeren-tial equations are equations in spaces of functions. We therefore shall, as we. An SIRS epidemic model, with a generalized nonlinear incidence as a function of the number of infected individuals, is developed and analyzed. Extending previous work, it is assumed that the natura.
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Rafael Ortega discussed the theory of twist maps with nonperiodic phase and presented applications. Peter Kloeden and Sylvia Novo showed how dynamical methods can be used to study the stability/bifurcation properties of bounded solutions and of attracting sets for nonautonomous differential and functional-differential equations.
Session "Stability and Bifurcation Problems for Non-Autonomous Differential Equations," held in Cetraro, Italy, June Anna Capietto and Jean Mawhin lectured on nonlinear boundary value problems; they applied the Maslov index and degree-theoretic methods in this Rating: % positive.
Stability and Bifurcation Theory for Non-Autonomous Differential Equations. by Russell Johnson,Maria Patrizia Pera,Sylvia Novo,Miguel Ortega,Jean Mawhin,Peter Kloeden,Anna Capietto.
Lecture Notes in Mathematics (Book ) Thanks for Sharing. You submitted the following rating and review. We'll publish them on our site once we've reviewed : Springer Berlin Heidelberg. Get this from a library. Stability and bifurcation theory for non-autonomous differential equations: Cetraro, Italy [Anna Capietto; Rafael Ortega; R Johnson; Maria Patrizia Pera; Peter E Kloeden; J Mawhin; Sylvia Novo;].
Lee "Stability and Bifurcation Theory for Non-Autonomous Differential Equations Cetraro, ItalyEditors: Russell Johnson, Maria Patrizia Pera" por Russell Johnson disponible en Rakuten Kobo.
This volume contains the notes from five lecture courses devoted to nonautonomous differential systems,Brand: Springer Berlin Heidelberg. Bifurcation theory is the mathematical study of changes in the qualitative or topological structure of a given family, such as the integral curves of a family of vector fields, and the solutions of a family of differential commonly applied to the mathematical study of dynamical systems, a bifurcation occurs when a small smooth change made to the parameter values (the bifurcation.
Topics under discussion include the Lyapunov stability of solutions, the existence and smoothness of invariant manifolds, and the construction and regularity of topological conjugacies. The exposition is directed to researchers as well as graduate students interested in differential equations and dynamical systems, particularly in stability theory.
The purpose of this book is to teach the theory of bifurcation of asymptotic solutions of evolution problems governed by nonlinear differential equations.
We have written this book for the broadest audience of potentially interested learners: engineers, biologists, chemists, physicists, mathematicians, economists, and others whose work involves.
Stability and Bifurcation Theory for Non-Autonomous Differential Equations Cetraro, ItalyEditors: Russell Johnson, Maria Patrizia Pera Scientific editor: R. Johnson, Universitá Firenze, Italy; M. Pera, Università degli Studi di Firenze, Italy This volume contains the notes from five lecture courses devoted to nonautonomous differential.
The courses took place during the C.I.M.E. Session "Stability and Bifurcation Problems for Non-Autonomous Differential Equations," held in Cetraro, Italy, June Anna Capietto and Jean Mawhin lectured on nonlinear boundary value problems; they applied the Maslov index and degree-theoretic methods in this context.
Two further kinds of developments will be mentioned briefly in the context of differential equations, though both can be taken further using difference Catastrophe Theory and Bifurcation (Routledge Revivals) DOI link for Catastrophe Theory and Bifurcation (Routledge Revivals) Catastrophe Theory and Bifurcation (Routledge Revivals) book.
Elementary Stability and Bifurcation Theory Temporarily out of stock. This substantially revised second edition teaches the bifurcation of asymptotic solutions to evolution problems governed by nonlinear differential s: 2.
Get this from a library. Stability and bifurcation theory for non-autonomous differential equations: Cetraro, Italy [Anna Capietto; R Johnson; Maria Patrizia Pera;] -- This volume contains the notes from five lecture courses devoted to nonautonomous differential systems, in which appropriate topological and dynamical techniques were described and applied to a.
Guckenheimer J, Holmes P () Nonlinear Oscillations, Dynamical Systems, and Bifurcation of Vector Fields, 2nd edn.
Hartman P () A lemma in the theory of structural stability of differential equations. Proc Am Math Soc Stepanov VV () Qualitative Theory of Differential Equations. Princeton Univ Press, Princeton Google. This was a good book.
Ir was above my expertise but was instructive nonetheless. It covered the usual value of linearization. It also covered perturbation methods then bifurcation theory (saddlenode, transcritical, pitchfork and Hopf) and then discusses chaos through the Reviews: 4. We study the phenomenon of stability breakdown for non-autonomous differential equations whose time dependence is determined by a minimal, strictly ergodic flow.
We find that, under appropriate assumptions, a new attractor may appear. More generally, almost automorphic minimal sets are found.
Before studying bifurcation I will start by analysing the stability of ordinary di erential equations both linear and non-linear with an arbitrary constant and look at how this constant a ects the stability of stationary points.
I will then go on to study bifurcation theory. In this project I will study the di erent types of bifurcations that. In regard to the stability of nonlinear systems, results of the linear theory are used to drive the results of Poincaré and Liapounoff.
Professor Bellman then surveys important results concerning the boundedness, stability, and asymptotic behavior of second-order linear differential s: 6. We extend a refined version of the subharmonic Melnikov method to piecewise-smooth systems and demonstrate the theory for bi- and trilinear oscillators.
Fundamental results for approximating solutions of piecewise-smooth systems by those of smooth systems are given and used to obtain the main result.
Special attention is paid to degenerate resonance behavior, and analytical results are. Main theme of this volume is the stability of nonautonomous differential equations, with emphasis on the Lyapunov stability of solutions, the existence and smoothness of invariant manifolds, the.Stability, Instability and Chaos - by Paul Glendinning November 9 - BIFURCATION THEORY II: PERIODIC ORBITS AND MAPS.
Paul Glendinning, University of Cambridge; the bifurcations of periodic orbits of differential equations and fixed points or periodic orbits of maps can be treated as one and the same topic.
As we saw in Chapter 6.An introduction to bifurcation theory Gr egory Faye1 1NeuroMathComp Laboratory, INRIA, Sophia Antipolis, CNRS, ENS Paris, France October 6, Abstract The aim of this chapter is to introduce tools from bifurcation theory which will be necessary in the following sections for the study of neural eld equations (NFE) set in the primary visual.