Related papers: Analytical results for coupled map lattices with l…
We examine the stationary--state equations for lattices with generalized Markovian dephasing and relaxation. When the Hamiltonian is quadratic, the single--particle correlation matrix has a closed system of equations even in the presence of…
We compare the behaviour of a small truncated coupled map lattice with random inputs at the boundaries with that of a large deterministic lattice essentially at the thermodynamic limit. We find exponential convergence for the probability…
Recent theoretical studies of statistical mechanical properties of systems with long range interactions are briefly reviewed. In these systems the interaction potential decays with a rate slower than 1/r^d at large distances r in d…
This is a significantly expanded version of the survey paper "Mixing and decay of correlations in non-uniformly expanding maps: a survey of recent results" math/0301319. We discuss recent results on decay of correlations for non-uniformly…
We consider diffusively coupled map lattices with $P$ neighbors (where $P$ is arbitrary) and study the stability of synchronized state. We show that there exists a critical lattice size beyond which the synchronized state is unstable. This…
Synchronization in an array of mutually coupled systems with a finite time-delay in coupling is studied using Josephson junction as a model system. The sum of the transverse Lyapunov exponents is evaluated as a function of the parameters by…
The effect of restricting the plaquette to be greater than a certain cutoff value is studied. The action considered is the standard Wilson action with the addition of a plaquette restriction, which should not affect the continuum limit of…
We study the completely synchronized states (CSSs) of a system of coupled logistic maps as a function of three parameters: interaction strength ($\varepsilon$), range of the interaction ($\alpha$), that can vary from first-neighbors to…
We present the linear-stability analysis of synchronised states in coupled time-delay systems. There exists a synchronisation threshold, for which we derive upper bounds, which does not depend on the delay time. We prove that at least for…
We show that in generic one-dimensional Hamiltonian lattices the diffusion coefficient of the maximum Lyapunov exponent diverges in the thermodynamic limit. We trace this back to the long-range correlations associated with the evolution of…
The scaling hypothesis for the coupled chotic map lattices (CML) is formulated. Scaling properties of the CML in the regime of extensive chaos observed numerically before is justified analytically. The asymptotic Liapunov exponents spectrum…
This study deals with analysis and control of cooperative synchronization for identical agents interacting on a directed graph topology. The agents are considered to have general continuous linear time-invariant dynamics with homogeneous…
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…
We consider an one-dimensional lattice system of unbounded and continuous spins. The Hamiltonian consists of a perturbed strictly-convex single-site potential and with longe-range interaction. We show that if the interactions decay…
The thermodynamic properties of dipolar spin ice on square, honeycomb and shakti lattices in the long-range and short-range dipole interaction models are studied. Exact solutions for the density of states, temperature dependencies of heat…
We study the synchronization of a linear array of globally coupled identical logistic maps. We consider a time-delayed coupling that takes into account the finite velocity of propagation of the interactions. We find globally synchronized…
Thermodynamic and dynamical properties of systems with long range pairwise interactions (LRI) which decay as 1/r^{d+\sigma} at large distances r in $d$ dimensions are reviewed in these Notes. Two broad classes of such systems are…
We show that long chaotic transients dominate the dynamics of randomly diluted networks of pulse-coupled oscillators. This contrasts with the rapid convergence towards limit cycle attractors found in networks of globally coupled units. The…
We study the coherent dynamics of globally coupled maps showing macroscopic chaos. With this term we indicate the hydrodynamical-like irregular behaviour of some global observables, with typical times much longer than the times related to…
We analyze, in general terms, the evolution of energy levels in quantum mechanics, as a function of a coupling parameter, and demonstrate the possibility of level crossings in systems described by irreducible matrices. In long-range…