Defect-mediated snaking: A new growth mechanism for localized structures
نویسندگان
چکیده
Stationary spatially localized patterns in parametrically driven systems are studied, focusing on the 2:1 and 1:1 resonance tongues as described by the forced complex Ginzburg–Landau equation. Homoclinic snaking is identified in both cases and the nature of the growth of the localized structures along the snaking branches is described. The structures grow from a central defect that inserts new rolls on either side, while pushing existing rolls outwards. This growth mechanism differs fundamentally from that found in other systems exhibiting homoclinic snaking in which new rolls are added at the fronts that connect the structure to the background homogeneous state. © 2010 Elsevier B.V. All rights reserved.
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 کاملWeakly subcritical stationary patterns: Eckhaus instability and homoclinic snaking.
The transition from subcritical to supercritical stationary periodic patterns is described by the one-dimensional cubic-quintic Ginzburg-Landau equation A(t) = μA + A(xx) + i(a(1)|A|(2)A(x) + a(2)A(2)A(x)*) + b|A|(2)|A - |A|(4)A, where A(x,t) represents the pattern amplitude and the coefficients μ, a(1), a(2), and b are real. The conditions for Eckhaus instability of periodic solutions are dete...
متن کاملAsymptotics of large bound states of localized structures.
We analyze stationary fronts connecting uniform and periodic states emerging from a pattern-forming instability. The size of the resulting periodic domains cannot be predicted with weakly nonlinear methods. We show that what determine this size are exponentially small (but exponentially growing in space) terms. These can only be computed by going beyond all orders of the usual multiple-scale ex...
متن کاملLocalized states in the conserved Swift-Hohenberg equation with cubic nonlinearity.
The conserved Swift-Hohenberg equation with cubic nonlinearity provides the simplest microscopic description of the thermodynamic transition from a fluid state to a crystalline state. The resulting phase field crystal model describes a variety of spatially localized structures, in addition to different spatially extended periodic structures. The location of these structures in the temperature v...
متن کاملForced Snaking
We study spatial localization in the real subcritical Ginzburg-Landau equation ut = m0u + Q(x)u + uxx + d|u|u − |u|u with spatially periodic forcing Q(x). When d > 0 and Q ≡ 0 this equation exhibits bistability between the trivial state u = 0 and a homogeneous nontrivial state u = u0 with stationary localized structures which accumulate at the Maxwell pointm0 = −3d/16. When spatial forcing is i...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010