Titlebook: Elements of Applied Bifurcation Theory; Yuri A. Kuznetsov Book 20043rd edition Springer Science+Business Media New York 2004 Mathematica.a

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https://doi.org/10.1007/978-981-19-1794-3 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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Bifurcations of Orbits Homoclinic and Heteroclinic to Hyperbolic Equilibria, dynamical systems. First we consider in detail two- and three-dimensional cases where geometrical intuition can be fully exploited. Then we show how to reduce generic .-dimensional cases to the considered ones plus a four-dimensional case treated in Appendix A.

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Other One-Parameter Bifurcations in Continuous-Time Dynamical Systems,urcations in symmetric systems, which are those systems that are invariant with respect to the representation of a certain symmetry group. After giving some general results on bifurcations in such systems, we restrict our attention to bifurcations of equilibria and cycles in the presence of the simp

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Numerical Analysis of Bifurcations,. Appendix B gives some background information on the bialternate matrix product used to detect Hopf and Neimark-Sacker bifurcations. Appendix C presents numerical methods for detection of higher-order homoclinic bifurcations. The bibliographical notes in Appendix D include references to standard no