Related papers: Pattern Dynamics of a Coupled Map Lattice for Open…
This paper presents a lattice approach to model the influence of cracking on inviscid flow in concrete. A mechanical lattice model based on a damage-plasticity constitutive model was combined with a new dual lattice of conduit elements for…
We show how a simple scheme of symbolic dynamics distinguishes a chaotic from a random time series and how it can be used to detect structural relationships in coupled dynamics. This is relevant for the question at which scale in complex…
We study the dynamics of an ensemble of globally coupled chaotic logistic maps under the action of a learning algorithm aimed at driving the system from incoherent collective evolution to a state of spontaneous full synchronization.…
A one-dimensional lattice model with mosaic quasiperiodic potential is found to exhibit interesting localization properties, e.g., clear mobility edges [Y. Wang et al., Phys. Rev. Lett. \textbf{125}, 196604 (2020)]. We generalize this…
Due to the deterministic nature of chaotic systems, fluctuations in their trajectories arise solely from the choice of initial conditions. Some of these dynamical fluctuations may lead to extremely unlikely scenarios. Understanding the…
Chaotic strings are particular classes of coupled map lattices that can serve as models for vacuum fluctuations in stochastically quantized field theories. They have been previously shown to distinguish standard model coupling parameters as…
We suggest an experimentally feasible procedure to observe paired and counterflow superfluidity in ultra-cold atom systems. We study the time evolution of one-dimensional mixtures of bosonic atoms in an optical lattice following an abrupt…
We study the spatial patterns formed by interacting biological populations or reacting chemicals under the influence of chaotic flows. Multiple species and nonlinear interactions are explicitly considered, as well as cases of smooth and…
We consider a diffusive Coupled Map Lattice (CML) for which the local map is piece-wise affine and has two stable fixed points. By introducing a spatio-temporal coding, we prove the one-to-one correspondence between the set of global orbits…
A system of five ordinary differential equations is studied which combines the Lorenz-84 model for the atmosphere and a box model for the ocean. The behaviour of this system is studied as a function of the coupling parameters. For most…
The affect of demographic stochasticity of a system of globally coupled chaotic maps is considered. A two-step model is studied, where the intra-patch chaotic dynamics is followed by a migration step that coupled all patches; the…
In this letter we study chaotic dynamical properties of an asymmetrically coupled one-dimensional chain of maps. We discuss the existence of coherent regions in terms of the presence of defects along the chain. We find out that temporal…
We study coupled maps on a Cayley tree, with local (nearest-neighbor) interactions, and with a variety of boundary conditions. The homogeneous state (where every lattice site has the same value) and the node-synchronized state (where sites…
In four-dimensional symplectic maps complex instability of periodic orbits is possible, which cannot occur in the two-dimensional case. We investigate the transition from stable to complex unstable dynamics of a fixed point under parameter…
Recent progress of symbolic dynamics of one- and especially two-dimensional maps has enabled us to construct symbolic dynamics for systems of ordinary differential equations (ODEs). Numerical study under the guidance of symbolic dynamics is…
Quantized, compact graphs were shown to be excellent paradigms for quantum chaos in bounded systems. Connecting them with leads to infinity we show that they display all the features which characterize scattering systems with an underlying…
We uncover and characterize different chaotic transport scenarios on perfect periodic surfaces by controlling the chaotic dynamics of particles subjected to periodic external forces in the absence of a ratchet effect. After identifying…
Networks having the geometry and the connectivity of trees are considered as the spatial support of spatiotemporal dynamical processes. A tree is characterized by two parameters: its ramification and its depth. The local dynamics at the…
Spatially-periodic patterns are studied in nonlocally coupled Gross-Pitaevskii equation. We show first that spatially periodic patterns appear in a model with the dipole-dipole interaction. Next, we study a model with a finite-range…
We investigate the synchronization phenomenon in coupled chaotic map lattices where the couplings decay with distance following a power-law. Depending on the lattice size, the coupling strength and the range of the interactions, complete…