منابع مشابه
Homoclinic Snakes Bounded by a Saddle-Center Periodic Orbit
We describe a new variant of the so-called homoclinic snaking mechanism for the generation of infinitely many distinct localized patterns in spatially reversible partial differential equations on the real line. In standard snaking a branch of localized states undergoes infinitely many folds as the pattern grows in length by adding cells at either side. In the cases studied here the localized st...
متن کاملBifurcations of a Homoclinic Orbit to Saddle-Center in Reversible Systems
and Applied Analysis 3 the unstable manifold in U0 by using the method introduced in Zhu 9 . According to the invariance and symmetry of these manifolds, we can deduce that system 2.1 has the following form inU0: ẋ x ( λ ( , μ ) O 1 ) , ẏ y −λ , μ O 1 , u̇ v ( ω ( , μ ) O 1 ) u ( O x O ( y ) O u ) O ( xy ) , v̇ u −ω , μ O 1 ) − vO x Oy O v ) −Oxy, 3.1 where λ 0, μ λ, ω 0, μ ω,O 1 O x O y O u O v ...
متن کاملA non - transverse homoclinic orbit to a saddle - node equilibrium .
Abst ract A homoclinic orbit is considered for which the center-stable and center-unstable manifolds of a saddle-node equilibrium have a quadratic tangency. This bifurcation is of codimension two and leads generically to the creation of a bifurcation curve deening two independent transverse homoclinic orbits to a saddle-node. This latter case was shown by L.P. Shilnikov to imply shift dynamics....
متن کاملMulti-round Homoclinic Orbits to a Hamiltonian with Saddle-center
We consider a real analytic, two degrees of freedom Hamiltonian system possessing a homoclinic orbit to a saddle-center equilibrium p (two nonzero real and two nonzero imaginary eigenvalues). We take a two-parameter unfolding for such the system and show that in nonresonance case there are countable sets of multiround homoclinic orbits to p. We also find families of periodic orbits, accumulatin...
متن کاملBifurcation from a Homoclinic Orbit in Partial Functional Differential Equations
We consider a family of partial functional differential equations which has a homoclinic orbit asymptotic to an isolated equilibrium point at a critical value of the parameter. Under some technical assumptions, we show that a unique stable periodic orbit bifurcates from the homoclinic orbit. Our approach follows the ideas of Šil’nikov for ordinary differential equations and of Chow and Deng for...
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ژورنال
عنوان ژورنال: Calculus of Variations and Partial Differential Equations
سال: 2003
ISSN: 0944-2669,1432-0835
DOI: 10.1007/s00526-002-0162-0