相关论文: Hierarchy of chaotic dynamics in random modular ne…
The effects of disorder in external forces on the dynamical behavior of coupled nonlinear oscillator networks are studied. When driven synchronously, i.e., all driving forces have the same phase, the networks display chaotic dynamics. We…
We provide appropriate tools for the analysis of dynamics and chaos for one-dimensional systems with periodic boundary conditions. Our approach allows for the investigation of the dependence of the largest Lyapunov exponent on various…
We study coupled dynamics on networks using symbolic dynamics. The symbolic dynamics is defined by dividing the state space into a small number of regions (typically 2), and considering the relative frequencies of the transitions between…
Spatially extended dynamical systems, namely coupled map lattices, driven by additive spatio-temporal noise are shown to exhibit stochastic synchronization. In analogy with low-dymensional systems, synchronization can be achieved only if…
We propose the existence of a new universality in classical chaotic systems when the number of degrees of freedom is large: the statistical property of the Lyapunov spectrum is described by Random Matrix Theory. We demonstrate it by…
In realistic neural circuits, both neurons and synapses are coupled in dynamics with separate time scales. The circuit functions are intimately related to these coupled dynamics. However, it remains challenging to understand the intrinsic…
In this paper we prove the propagation of chaos property for an ensemble of interacting neurons subject to independent Brownian noise. The propagation of chaos property means that in the large network size limit, the neurons behave as if…
Network of nonlinear dynamical elements often show clustering of synchronization by chaotic instability. Relevance of the clustering to ecological, immune, neural, and cellular networks is discussed, with the emphasis of partially ordered…
Chaotic functions are characterized by sensitivity to initial conditions, transitivity, and regularity. Providing new functions with such properties is a real challenge. This work shows that one can associate with any Boolean network a…
In many complex systems, elementary units live in a chaotic environment and need to adapt their strategies to perform a task, by extracting information from the environment and controlling the feedback loop on it. One of the main example of…
We study the mean-field limit and stationary distributions of a pulse-coupled network modeling the dynamics of a large neuronal assemblies. Our model takes into account explicitly the intrinsic randomness of firing times, contrasting with…
Population dynamics in random ecological networks are investigated by analyzing a simple deterministic equation. It is found that a sequence of abrupt changes of populations punctuating quiescent states characterize the long time behavior.…
High-dimensional data must be highly structured to be learnable. Although the compositional and hierarchical nature of data is often put forward to explain learnability, quantitative measurements establishing these properties are scarce.…
We consider an infinite network of globally-coupled phase oscillators in which the natural frequencies of the oscillators are drawn from a symmetric bimodal distribution. We demonstrate that macroscopic chaos can occur in this system when…
Realistic networks display heterogeneous transmission delays. We analyze here the limits of large stochastic multi-populations networks with stochastic coupling and random interconnection delays. We show that depending on the nature of the…
We propose to control the orbits of the two-dimensional Rulkov model affected by bounded noise. For the correct parameter choice the phase space presents two chaotic regions separated by a transient chaotic region in between. One of the…
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…
Phase-coupled oscillators serve as paradigmatic models of networks of weakly interacting oscillatory units in physics and biology. The order parameter which quantifies synchronization was so far found to be chaotic only in systems with…
High-dimensional dynamical systems of interacting degrees of freedom are ubiquitous in the study of complex systems. When the directed interactions are totally uncorrelated, sufficiently strong and non-linear, many of these systems exhibit…
We develop a formalism to describe the discrete-time dynamics of systems containing an arbitrary number of interacting species. The individual-based model, which forms our starting point, is described by a Markov chain, which in the limit…