Related papers: Collective Behavior of Coupled Chaotic Maps
We study the peculiarities of the solitary state appearance in the ensemble of nonlocally coupled chaotic maps. We show that nonlocal coupling and features of the partial elements lead to arising of multistability in the system. The…
Chaotic dynamics can be quite heterogeneous in the sense that in some regions the dynamics are unstable in more directions than in other regions. When trajectories wander between these regions, the dynamics is complicated. We say a chaotic…
The Lyapunov exponent for collective motion is defined in order to characterize chaotic properties of collective motion for large populations of chaotic elements. Numerical computations for this quantity suggest that such collective motion…
A novel type of self-organized lattice in which chaotic defects are arranged periodically is reported for a coupled map model of open flow. We find that temporally chaotic defects are followed by spatial relaxation to an almost periodic…
In the turbulent regime of coupled map lattice with non-local interaction the maps systematically form periodic cluster attractors and their remnants by synchronization due to the foliation of periodic windows of the element map. We examine…
Relationships between a chaotic behavior and closely related properties of topological transitivity, sensitivity to initial conditions, density of closed orbits of homeomorphism groups and their countable products are investigated. We…
We discovered numerically a scaling law obeyed by the amplitude of collective mo tion in large populations of chaotic elements. Our analysis strongly suggests that such populations generically exhibit collective motion in the presence of…
A nonuniform system is considered consisting of two phases with different densities of particles. At each given time the distribution of the phases in space is chaotic: each phase filling a set of regions with random shapes and locations. A…
We propose a new method to investigate collective behavior in a network of globally coupled chaotic elements generated by a tent map. In the limit of large system size, the dynamics is described with the nonlinear Frobenius-Perron equation.…
An algorithm to characterize collective motion is presented, with the introduction of ``collective Lyapunov exponent'', as the orbital instability at a macroscopic level. By applying the algorithm to a globally coupled map, existence of…
We review recent numerical studies and the phenomenology of spatially synchronized collective states in many-body dynamical systems. These states exhibit thermodynamic noise superimposed on the collective, quasiperiodic order parameter…
Traveling waves triggered by a phase slip in coupled map lattices are studied. A local phase slip affects globally the system, which is in strong contrast with kink propagation. Attractors with different velocities coexist, and form…
In this work we investigate the spatiotemporal behaviour of lattices of coupled chaotic logistic maps, where the coupling between sites has a nonlinear form. We show that the stable range of the spatiotemporal fixed point state is…
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 discuss how to characterize the behavior of a chaotic dynamical system depending on a parameter that varies periodically in time. In particular, we study the predictability time, the correlations and the mean responses, by defining a…
Collective stable chaos consists of the persistence of disordered patterns in dynamical spatiotemporal systems possessing a negative maximum Lyapunov exponent. We analyze the role of the topology of connectivity on the emergence and…
Dynamical fluctuations or rare events associated with atypical trajectories in chaotic maps due to specific initial conditions can crucially determine their fate, as the may lead to stability islands or regions in phase space otherwise…
Bifurcations in a system of coupled maps are investigated. Using symbolic dynamics it is proven that for coupled shift maps the well known space--time--mixing attractor becomes unstable at a critical coupling strength in favour of a…
A network of $N$ elements is studied in terms of a deterministic globally coupled map which can be chaotic. There exists a range of values for the parameters of the map where the number of different macroscopic configurations is very large,…
Chaotic dynamics is always characterized by swarms of unstable trajectories, unpredictable individually, and thus generally studied statistically. It is often the case that such phase-space densities relax exponentially fast to a limiting…