Abstract
In this chapter we formulate conditions defining the simplest bifurcations of equilibria in n-dimensional continuous-time systems: the fold and the Hopf bifurcations. Then we study these bifurcations in the lowest possible dimensions: the fold bifurcation for scalar systems and the Hopf bifurcation for planar systems. Chapter 5 shows how to “lift” these results to n-dimensional situations.
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© 1995 Springer Science+Business Media New York
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Kuznetsov, Y.A. (1995). One-Parameter Bifurcations of Equilibria in Continuous-Time Systems. In: Elements of Applied Bifurcation Theory. Applied Mathematical Sciences, vol 112. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-2421-9_3
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DOI: https://doi.org/10.1007/978-1-4757-2421-9_3
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4757-2423-3
Online ISBN: 978-1-4757-2421-9
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