منابع مشابه
Imperfect homoclinic bifurcations.
Experimental observations of an almost symmetric electronic circuit show complicated sequences of bifurcations. These results are discussed in the light of a theory of imperfect global bifurcations. It is shown that much of the dynamics observed in the circuit can be understood by reference to imperfect homoclinic bifurcations without constructing an explicit mathematical model of the system.
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1. Introduction. We say that a one-parameter family of diffeomorphisms ip^: M — • M, p G R, has a homoclinic bifurcation, or a homoclinic tangency, for p = 0 if ipo has an orbit of nontransverse intersection of a stable and an unstable manifold, both of the same hyperbolic fixed point (or periodic point), which splits, for p > 0, into two orbits of transverse intersection of these stable and un...
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Homoclinic orbits to bifocus-type stationary points have been studied theoretically by a number of authors, but up until now, only one analytic example has been found. In this paper we summarise and extend the known theory regarding bifocal homoclinic bifurcations and present numerical verification of some of the more interesting theoretical predictions that have been made.
متن کاملResonant homoclinic ip bifurcations
This paper studies three-parameter unfoldings of resonant orbit ip and inclination ip homoclinic orbits. First all known results on codimension-two unfoldings of homoclinic ip bifurcations are presented. Then we show that the orbit ip and inclination ip both feature the creation and destruction of a cusp horseshoe. Furthermore, we show near which resonant ip bifurcations a homoclinic-doubling c...
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The thesis investigates bifurcations from homoclinic solutions of ordinary differential equations. Homoclinic solutions are characterised by approaching an equilibrium, i.e. a constant solution of a differential equation, in both positive and negative time. The thesis is devoted to the analysis of homoclinic bifurcations that originate from a change in the type of the associated equilibrium. Se...
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ژورنال
عنوان ژورنال: Physical Review E
سال: 2001
ISSN: 1063-651X,1095-3787
DOI: 10.1103/physreve.64.036208