Titlebook: Elements of Applied Bifurcation Theory; Yuri A. Kuznetsov Book 19982nd edition Springer-Verlag New York 1998 bifurcation.dynamical systems

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Commonwealth of Independent States,r the final two bifurcations in the previous chapter, the description of the majority of these bifurcations is incomplete in principle. For all but two cases, only . normal forms can be constructed. Some of these normal forms will be presented in terms of associated planar continuous-time systems wh

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Adnan Badran,Elias Baydoun,John R. Hillman routines like those for solving linear systems, finding eigenvectors and eigenvalues, and performing numerical integration of ODEs are known to the reader. Instead we focus on algorithms that are more specific to bifurcation analysis, specifically those for the location of equilibria (fixed points)

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Elements of Applied Bifurcation Theory978-0-387-22710-8Series ISSN 0066-5452 Series E-ISSN 2196-968X

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Yuri A. KuznetsovDynamical systems continues to be a topic of current interest in mathematics, engineering, and physics..This modern approach provides the reader with a solid basis in dynamical systems theory and the

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Bifurcations of Equilibria and Periodic Orbits in ,-Dimensional Dynamical Systems, we derive explicit formulas for the approximation of center manifolds in finite dimensions and for systems restricted to them at bifurcation parameter values. In Appendix 1 we consider a reaction-diffusion system on an interval to illustrate the necessary modifications of the technique to handle infinite-dimensional systems.

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Introduction to Dynamical Systems,scovered in the 1960s that rather simple dynamical systems may behave “randomly,” or “chaotically.” Finally, we discuss how differential equations can define dynamical systems in both finite- and infinite-dimensional spaces.