Spatiotemporal chaos in terms of unstable recurrent patterns
نویسنده
چکیده
Spatiotemporally chaotic dynamics of a Kuramoto–Sivashinsky system is described by means of an infinite hierarchy of its unstable spatiotemporally periodic solutions. An intrinsic parametrization of the corresponding invariant set serves as an accurate guide to the highdimensional dynamics, and the periodic orbit theory yields several global averages characterizing the chaotic dynamics. PACS numbers: 0230J, 0320, 0340, 0545
منابع مشابه
ar X iv : c ha o - dy n / 96 06 01 6 v 1 1 J ul 1 99 6 Hopf ’ s last hope : spatiotemporal chaos in terms of unstable recurrent patterns
Spatiotemporally chaotic dynamics of a Kuramoto-Sivashinsky system is described by means of an infinite hierarchy of its unstable spatiotemporally periodic solutions. An intrinsic parametrization of the corresponding invariant set serves as accurate guide to the high-dimensional dynamics, and the periodic orbit theory yields several global averages characterizing the chaotic dynamics.
متن کاملHopf ' s last hope : spatiotemporal chaos in terms ofunstable recurrent
Spatiotemporally chaotic dynamics of a Kuramoto-Sivashinsky system is described by means of an innnite hierarchy of its unstable spatiotemporally periodic solutions. An intrinsic parametrization of the corresponding invariant set serves as accurate guide to the high-dimensional dynamics, and the periodic orbit theory yields several global averages characterizing the chaotic dynamics.
متن کاملControlling Spatiotemporal Chaos in One- and Two-Dimensional Coupled Logistic Map Lattices
A method of control of spatiotemporal chaos in lattices of coupled maps is proposed in this work. Forms of spatiotemporal perturbations of a system parameter are analytically determined for oneand twodimensional logistic map lattices with different kinds of coupling to stabilize chosen spatiotemporal states previously unstable. The results are illustrated by numerical simulation. Controlled tra...
متن کاملCharacterization of spatiotemporal chaos in an inhomogeneous active medium
We study a reaction diffusion system of the activator-inhibitor type with inhomogeneous reaction terms showing spatiotemporal chaos. We analyze the topological properties of the unstable periodic orbits in the slow chaotic dynamics appearing, which can be embedded in three dimensions. We perform a bi-orthogonal decomposition analyzing the minimum number of modes necessary to find the same organ...
متن کاملNonlinear Diiusion Control of Spatiotemporal Chaos in the Complex Ginzburg Landau Equation Typeset Using Revt E X
The role of nonlinear diiusion terms in the stability of periodic solutions in the regime of spatio temporal chaos is studied. The stabilization of unstable plane waves in the Complex Ginzburg Landau equation in weakly chaotic regimes such as phase turbulence and spatiotemporal intermittency or in strong chaotic ones like defect turbulence is demonstrated.
متن کامل