1,721,017 research outputs found
Tori Breakdown in coupled map lattice
No full textWe present a numerical study of the behaviour and breakdown of tori in a lattice of diffusively coupled logistic maps
Behavior of a Three-Torus in Truncated Navier-Stokes Equations
No full textThe presence of a three-torus in a seven-mode truncation of the three-dimensional Navier-Stokes equations is investigated numerically by means of cross-section and power spectra. Furthermore, by taking advantage of particular features of the model, rotation vectors, circle maps and torus maps can be computed with high accuracy and used to study the dynamics. In particular, some interesting phenomena of partial phase-locking are described in deep detail. The three-torus, which arises via a Hopf bifurcation and persists in a wide parameter range, is found to break and originate a strange attractor. The onset of chaos and the associated bifurcation point can be defined quite precisely
Tori breakdown in coupled map lattices
No full textIn this paper we present a numerical study of invariant tori in a lattice of coupled logistic maps. In particular, we are interested in bifurcations leading to chaos. Here we consider six different examples of tori breakdown: two of them completely confirm the theory of Afraimovich and Shilnikov, while the others appear peculiar to the model
Bifurcation of Homogeneous Solutions in a Chain of Logistic Maps
No full textIn this paper we study the bifurcation of the homogeneous fixed point of a lattice of n diffusively coupled logistic maps. An analytical computation of the reduced map on the centermanifold is performed by taking into account the symmetries of the system. If n is even, a subcritical flip bifurcation causes a symmetry breaking of the homogeneous pattern whichproduces a traveling (rotating) wave with velocity 1 and time period 2. For odd n, since the bifurcation has a two dimensional normal form, we limit ourselves to consider only the simplest case (n = 3). In this case, a supercritical flip bifurcation is observed; three less symmetric periodic orbits of time period 2 are generated by the breaking of the homogeneous orbit. However, the bifurcation is rather degenerate and we have numerical hints that a second family of asymmetric periodic points is generated. Some details, pertaining to the dynamicsof the truncated map on the two dimensional center manifold for n = 3, are also presented
Numerical study of ground state energy fluctuations in spin glasses
No full textUsing a stochastic algorithm introduced in a previous paper, we study the finite size volume corrections and the fluctuations of the ground state energy in the Sherrington-Kirkpatrick and the Edwards-Anderson models at zero temperature. The algorithm is based on a suitable annealing procedure coupled with a balanced greedy-reluctant strategy that drives the systems towards the deepest minimum of the energy function
On the presence of Normally Atracting Manifolds Containing Periodic or Quasiperiodic Orbits in Coupled Map Lattices
No full textThe 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
Qualitative and Quantitative Stabilized Behavior of Truncated Two-Dimensional Navier-Stokes Equations
No full textN-mode truncations of the Navier-Stokes equations on a two-dimensional torus are investigated for increasing N, up to a maximum of N=1000. A parameter range is considered in which the behavior is first quasi-periodic and then chaotic. A Poincaré map analysis shows features which clearly stabilize as N increases, from both a qualitative and quantitative point of view. Concerning the onset of chaos, it is found that the appearance of bumps and foldings in the section curve is the cause of the breaking of the torus. A detailed description of the transition is given for N=502
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