The significant presence of normally attracting invariant manifolds, formed by closed curves or two-tori, is investigated in two-dimensional lattices of coupled chaotic maps. In the case of a manifold formed by closed curves, it contains symmetrically placed periodic orbits, with the property of a very weak hyperbolicity along the manifold itself. The resulting dynamics is an extremely slow relaxation to periodic behavior. Analogously, a manifold consisting of two-tori includes very weakly hyperbolic periodic (or quasiperiodic) orbits, which in this case also implies quite a long time before any solution approaches periodicity or quasiperiodicity.The normally attracting manifolds and the contained weak attractors can undergo several global bifurcations. Some of them, including saddle-node bifurcation, period-doubling and Hopf bifurcation, are illustrated.Almost all the asymptotic solutions that we discuss have flat rows or flat columns, which means that they can occur also in one-dimensional lattices.

On the presence of Normally Atracting Manifolds Containing Periodic or Quasiperiodic Orbits in Coupled Map Lattices / Giberti, Claudio; Vernia, Cecilia. - In: INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS IN APPLIED SCIENCES AND ENGINEERING. - ISSN 0218-1274. - STAMPA. - 3:(1993), pp. 1503-1514.

On the presence of Normally Atracting Manifolds Containing Periodic or Quasiperiodic Orbits in Coupled Map Lattices

GIBERTI, Claudio;VERNIA, Cecilia
1993

Abstract

The significant presence of normally attracting invariant manifolds, formed by closed curves or two-tori, is investigated in two-dimensional lattices of coupled chaotic maps. In the case of a manifold formed by closed curves, it contains symmetrically placed periodic orbits, with the property of a very weak hyperbolicity along the manifold itself. The resulting dynamics is an extremely slow relaxation to periodic behavior. Analogously, a manifold consisting of two-tori includes very weakly hyperbolic periodic (or quasiperiodic) orbits, which in this case also implies quite a long time before any solution approaches periodicity or quasiperiodicity.The normally attracting manifolds and the contained weak attractors can undergo several global bifurcations. Some of them, including saddle-node bifurcation, period-doubling and Hopf bifurcation, are illustrated.Almost all the asymptotic solutions that we discuss have flat rows or flat columns, which means that they can occur also in one-dimensional lattices.
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1503
1514
On the presence of Normally Atracting Manifolds Containing Periodic or Quasiperiodic Orbits in Coupled Map Lattices / Giberti, Claudio; Vernia, Cecilia. - In: INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS IN APPLIED SCIENCES AND ENGINEERING. - ISSN 0218-1274. - STAMPA. - 3:(1993), pp. 1503-1514.
Giberti, Claudio; Vernia, Cecilia
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/611771
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