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

泄露

Alessandro Caroli,Stefano Zanasié-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

执

Kienböck’s Disease and Ulnar Variancetor fields have the common property that they are defined in terms of functions; however, their flows are completely different. While periodic and homoclinic orbits may be omnipresent in conservative systems, the limit sets of orbits of gradient systems are necessarily part of the set of equilibria.

合法

contrast-medium

宽宏大量

Evolution of Quantitative Easingstudy of dynamics and bifurcations of maps. In particular, we investigate local bifurcations of a class of maps, monotone maps, which will later play a prominent role in our study of differential equations. We end the chapter with a brief exposition of a landmark quadratic map, the logistic map.

locus-ceruleus

起草

JIBE

A. Herbert Alexander,David M. Lichtman orbit encircling the equilibrium point. We present a proof of this celebrated result—the Poincaré-Andronov-Hopf Theorem—and a discussion of the stability of the periodic orbit. We conclude with an exposition of computational procedures for determining bifurcation diagrams of periodic orbits bifurca

harrow

Kienböck’s Disease and Ulnar Variancerst present several basic theorems on the presence or absence of periodic orbits of planar systems. We then investigate the stability and local bifurcations of periodic orbits in terms of Poincaré maps. As an important application of these ideas, we establish the existence of a globally attracting p

自爱