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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© 1998 Springer-Verlag New York, Inc.
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(1998). One-Parameter Bifurcations of Equilibria in Continuous-Time Dynamical Systems. In: Elements of Applied Bifurcation Theory. Applied Mathematical Sciences, vol 112. Springer, New York, NY. https://doi.org/10.1007/978-0-387-22710-8_3
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DOI: https://doi.org/10.1007/978-0-387-22710-8_3
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-98382-0
Online ISBN: 978-0-387-22710-8
eBook Packages: Springer Book Archive