Related papers: Fuzzy phase transition in a 1D coupled stable-map …
We investigate the processes of synchronization and phase ordering in a system of globally coupled maps possessing bistable, chaotic local dynamics. The stability boundaries of the synchronized states are determined on the space of…
An attractor of a piecewise-smooth continuous system of differential equations can bifurcate from a stable equilibrium to a more complicated invariant set when it collides with a switching manifold under parameter variation. Here numerical…
The collective behavior of a coupled map lattice having {\it unbounded} chaotic local dynamics is investigated through the properties of its mean field. The presence of unstable periodic orbits in the local maps determines the emergence of…
Dynamics of coupled chaotic oscillators on a network are studied using coupled maps. Within a broad range of parameter values representing the coupling strength or the degree of elements, the system repeats formation and split of coherent…
Dynamical scaling in a two-dimensional lattice model of chaotic maps, in contact with a thermal bath, is numerically studied. The model here proposed is equivalent to a conserved Ising model with coupligs which fluctuate over the same time…
By using the kicked Harper model, the effect of dynamical perturbations to the localized and ballistic phases in aperiodic lattice systems is investigated. The transition from the localized phase to diffusive phase via a critical…
Different scenarios of the fluctuation-induced disordering of the striped phase which is formed at low temperatures in the triangular-lattice Ising model with the antiferromagnetic interaction of nearest and next-to-nearest neighbors are…
The vortex lattice is an ideal system to study the competition and interplay between interaction and disorder. New results on 2H-NbSe_2 (in samples of progressively increasing pinning) elucidate how pinning alters the phase boundary…
Coupled map lattices of non-hyperbolic local maps arise naturally in many physical situations described by discretised reaction diffusion equations or discretised scalar field theories. As a prototype for these types of lattice dynamical…
We study the evolution of the dynamics across a generic first order quantum phase transition in an interacting boson model of nuclei. The dynamics inside the phase coexistence region exhibits a very simple pattern. A classical analysis…
Complex patterns generated by the time evolution of a one-dimensional digitalized coupled map lattice are quantitatively analyzed. A method for discerning complexity among the different patterns is implemented. The quantitative results…
Spectral properties of Coupled Map Lattices are described. Conditions for the stability of spatially homogeneous chaotic solutions are derived using linear stability analysis. Global stability analysis results are also presented. The…
Phase transitions of the mixed spin-1/2 and spin-1 Ising-Heisenberg model on several decorated planar lattices consisting of interconnected diamonds are investigated within the framework of the generalized decoration-iteration…
A recently introduced lattice model, describing an extended system which exhibits a reentrant (symmetry-breaking, second-order) noise-induced nonequilibrium phase transition, is studied under the assumption that the multiplicative noise…
The dynamics of nonlocally coupled dissipative kicked rotors is rich and complex. In this study, we consider a network of rotors where each interacts equally with a certain range of its neighbors. We focus on the influence of the coupling…
We study synchronization of low-dimensional ($d=2,3,4$) chaotic piecewise linear maps. For Bernoulli maps we find Lyapunov exponents and locate the synchronization transition, that numerically is found to be discontinuous (despite…
Order-disorder transitions take place in many physical systems, but observing them in detail in real materials is difficult. In two- or quasi-two-dimensional systems, the transition has been studied by computer simulations and…
We demonstrate the existence of a new topologically ordered phase in Kitaev's honeycomb lattice model. This new phase appears due to the presence of a vortex lattice and it supports chiral Abelian anyons. We characterize the phase by its…
Several theorems are demonstrated that determine the sufficient conditions for the existence of synchronized states (periodical and chaotic) and also of travelling waves in a CML. Also are analytically proven the existence of…
We show that, in periodically perturbed chaotic systems, Phase Synchronization appears, associated to a special type of stroboscopic map, in which not only averages quantities are equal to invariants of the perturbation, the angular…