Related papers: Bifurcations in Globally Coupled Chaotic Maps
The dynamics of globally coupled map lattices can be described in terms of a nonlinear Frobenius--Perron equation in the limit of large system size. This approach allows for an analytical computation of stationary states and their…
Fluctuations of the mean field of a globally coupled dynamical systems are discussed. The origin of hidden coherence is related with the instability of the fixed point solution of the self-consistent Perron-Frobenius equation. Collective…
A mean-field formulation is used to investigate the bifurcation diagram for globally coupled tent maps by means of an analytical approach. It is shown that the period doubling sequence of the single site map induces a continuous family of…
Collective behavior is studied in globally coupled maps with distributed nonlinearity. It is shown that the heterogeneity enhances regularity in the collective dynamics. Low-dimensional quasiperiodic motion is often found for the…
The emergence of nontrivial collective behavior in networks of coupled chaotic maps is investigated by means of a nonlinear mutual prediction method. The resulting prediction error is used to measure the amount of information that a local…
Collective behavior is studied in globally coupled maps. Several coherent motions exist, even in fully desynchronized state. To characterize the collective behavior, we introduce scaling transformation of parameter, and detect the…
We show, using generic globally-coupled systems, that the collective dynamics of large chaotic systems is encoded in their Lyapunov spectra: most modes are typically localized on a few degrees of freedom, but some are delocalized, acting…
We show, using covariant Lyapunov vectors in addition to standard Lyapunov analysis, that there exists a set of collective Lyapunov modes in large chaotic systems exhibiting collective dynamics. Associated with delocalized Lyapunov vectors,…
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…
We study a generalization of globally coupled maps, where the elements are updated with probability $p$. When $p$ is below a threshold $p_c$, the collective motion vanishes and the system is the stationary state in the large size limit. We…
The phenomena of synchronization and nontrivial collective behavior are studied in a model of coupled chaotic maps with random global coupling. The mean field of the system is coupled to a fraction of elements randomly chosen at any given…
We report in this paper a complete analytical study on the bifurcations and chaotic phenomena observed in certain second-order, non-autonomous, dissipative chaotic systems. One-parameter bifurcation diagrams obtained from the analytical…
A method to predict the emergence of different kinds of ordered collective behaviors in systems of globally coupled chaotic maps is proposed. The method is based on the analogy between globally coupled maps and a map subjected to an…
We study systems of globally coupled interval maps, where the identical individual maps have two expanding, fractional linear, onto branches, and where the coupling is introduced via a parameter - common to all individual maps - that…
We study synchronization of non-diffusively coupled map networks with arbitrary network topologies, where the connections between different units are, in general, not symmetric and can carry both positive and negative weights. We show that,…
This paper describes the design of a modified tent map characterized by a uniform probability density function. The use of this map is proposed as an alternative to the tent map and the Bernoulli shift. It is shown that practical circuits…
We study emergent oscillatory behavior in networks of diffusively coupled nonlinear ordinary differential equations. Starting from a situation where each isolated node possesses a globally attracting equilibrium point, we give, for an…
For a system of globally coupled chaotic maps with bistable behaviour we relate the rate function for large deviations in the system size at finite time to dynamical properties of the self consistent Perron-Frobenius operator (SCPFO) that…
We introduce a new method for determining the global stability of synchronization in systems of coupled identical maps. The method is based on the study of invariant measures. Besides the simplest non-trivial example, namely two…
The phenomenon of turbulence is investigated in the context of globally coupled maps. The local dynamics is given by the Chat\'e-Manneville minimal map previously used in studies of spatiotemporal intermittency in locally coupled map…