Related papers: Globally coupled chaotic maps with bistable behavi…
We study the transition to synchronization in large, dense networks of chaotic circle maps, where an exact solution of the mean-field dynamics in the infinite network and all-to-all coupling limit is known. In dense networks of finite size…
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…
The linear response of synchronized chaotic units with delayed couplings and feedback to small external perturbations is investigated in the context of communication with chaos synchronization. For iterated chaotic maps, the distribution of…
One of the common characteristics of chaotic maps or flows in high dimensions is "unstable dimensional variability", in which there are periodic points whose unstable manifolds have different dimensions. In this paper, in trying to…
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 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…
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…
The study of escape rates for a ball in a dynamical systems has been much studied. Understanding the asymptotic behavior of the escape rate as the radius of the ball tends to zero is an especially subtle problem. In the case of hyperbolic…
Dynamics in biological networks are in general robust against several perturbations. We investigate a coupled map network as a model motivated by gene regulatory networks and design systems which are robust against phenotypic perturbations…
We investigate the phenomenon of chaos synchronization in systems subject to coexisting autonomous and external global fields by employing a simple model of coupled maps. Two states of chaos synchronization are found: (i) complete…
Effect of noise in inducing order on various chaotically evolving systems is reviewed, with special emphasis on systems consisting of coupled chaotic elements. In many situations it is observed that the uncoupled elements when driven by…
The spectral two-point function of chaotic quantum graphs is expected to be universal. Within the supersymmetry approach, a proof of that assertion amounts to showing that the contribution of non-universal (or massive) modes vanishes in the…
We consider a perturbed system $(X,\varphi(\epsilon,\cdot))$, where $X$ is a topological Markov shift with a countably infinite state space, and $\varphi(\epsilon,\cdot)$ is a real-valued potential on X depending on a small parameter…
A topological bifurcation in chaotic scattering is characterized by a sudden change in the topology of the infinite set of unstable periodic orbits embedded in the underlying chaotic invariant set. We uncover a scaling law for the fractal…
The phase ordering dynamics of coupled chaotic maps on fractal networks are investigated. The statistical properties of the systems are characterized by means of the persistence probability of equivalent spin variables that define the…
In this note we present two types of biological models which have interesting ergodic and chaotic properties. The first type are one-dimensional transformations, like a logistic map, which are used to describe the change in population size…
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…
New aspects of spectral fluctuations of (quantum) chaotic and diffusive systems are considered, namely autocorrelations of the spacing between consecutive levels or spacing autocovariances. They can be viewed as a discretized two point…
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…
We explore the concept of metastability in random dynamical systems, focussing on connections between random Perron-Frobenius operator cocycles and escape rates of random maps, and on topological entropy of random shifts of finite type. The…