Abstract
This chapter is devoted to generic bifurcations of equilibria in two-parameter systems of differential equations. First, we make a complete list of such bifurcations. Then, we derive a parameter-dependent normal form for each bifurcation in the minimal possible phase dimension and specify relevant nondegeneracy conditions. Next, we truncate higher-order terms and present the bifurcation diagrams of the resulting system. The analysis is completed by a discussion of the effect of the higher-order terms. In those cases where the higher-order terms do not qualitatively alter the bifurcation diagram, the truncated systems provide topological normal forms for the relevant bifurcations. The results of this chapter can be applied to n-dimensional systems by means of the parameter-dependent version of the Center Manifold Theorem (see Chapter 5).
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© 1995 Springer Science+Business Media New York
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Kuznetsov, Y.A. (1995). Two-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/10.1007/978-1-4757-2421-9_8
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DOI: https://doi.org/10.1007/978-1-4757-2421-9_8
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4757-2423-3
Online ISBN: 978-1-4757-2421-9
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