Titlebook: Dynamics and Bifurcations; Jack K. Hale,Hüseyin Koçak Textbook 1991 Springer-Verlag New York, Inc. 1991 Eigenvalue.bifurcation.difference

菊花

In the Presence of Purely Imaginary Eigenvaluese the linearized vector field has purely imaginary eigenvalues. Using polar coordinates, we capture the dynamics of such a system in the neighborhood of the equilibrium point in terms of the dynamics of an appropriate nonautonomous scalar differentia] equation with periodic coefficients. For the ana

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合同

All Planar Things Consideredé-Andronov-Hopf, and breaking homoclinic loops and saddle connections. It is natural to ponder when, if ever, we will stop adding to the list and produce a complete catalog of all possible bifurcations. In this chapter, we indeed provide such a list for “generic” bifurcations of planar vector fields

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Planar Mapsd bifurcations of planar maps. Our motives for delving into planar maps arc akin to the ones for studying scalar maps; namely, as numerical approximations of solutions of differential equations or as Poincaré maps. We begin our exposition with an introduction to the dynamics of linear planar maps. T

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tolerance

https://doi.org/10.1007/978-1-4612-4426-4Eigenvalue; bifurcation; difference equation; dynamical systems; stability

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Decline of the Yangtze River Civilization from technical complications, the setting is one-dimensional—the scalar autonomous differential equations. Despite their simplicity, these concepts are central to our subject and reappear in various incarnations throughout the book. Following a collection of examples, we first state a theorem on th

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