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Employing efficient diagonalization techniques, we perform a detailed quantitative study of the regular and chaotic regions in phase space in the simplest non-integrable atom-field system, the Dicke model. A close correlation between the…

This paper is a review dealing with the study of large size random recurrent neural networks. The connection weights are selected according to a probability law and it is possible to predict the network dynamics at a macroscopic scale using…

A procedure to characterize chaotic dynamical systems with concepts of complex networks is pursued, in which a dynamical system is mapped onto a network. The nodes represent the regions of space visited by the system, while edges represent…

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,…

The research concerns the dynamics of complex autonomous Kauffman networks. The article defines and shows using simulation experiments half-chaotic networks, which exhibit features much more similar to typically modeled systems like a…

We propose a mechanism which produces periodic variations of the degree of predictability in dynamical systems. It is shown that even in the absence of noise when the control parameter changes periodically in time, below and above the…

We propose a mechanism by which the efficiency of mixing in chaotic flows can be enhanced. Our mechanism consists of introducing small changes in the system parameters in regions of phase space where the local Lyapunov exponent falls…

Characterizing the in uence of network properties on the global emerging behavior of interacting elements constitutes a central question in many areas, from physical to social sciences. In this article we study a primary model of disordered…

We show that long chaotic transients dominate the dynamics of randomly diluted networks of pulse-coupled oscillators. This contrasts with the rapid convergence towards limit cycle attractors found in networks of globally coupled units. The…

We propose a stochastic dynamical model of noisy neural networks with complex architectures and discuss activation of neural networks by a stimulus, pacemakers and spontaneous activity. This model has a complex phase diagram with…

The route to chaos and phase dynamics in a rotating shallow-water model were rigorously examined using a five-mode Galerkin truncated system with complex variables. This system is valuable for investigating how large/meso-scales destabilize…

Chaos and unpredictability are traditionally synonymous, yet large-scale machine learning methods recently have demonstrated a surprising ability to forecast chaotic systems well beyond typical predictability horizons. However, recent works…

Characterizing accurately chaotic behaviors is not a trivial problem and must allow to determine the properties that two given chaotic invariant sets share or not. The underlying problem is the classification of chaotic regimes, and their…

We disclose a new class of patterns, called patched patterns, in arrays of non-locally coupled excitable units with attractive and repulsive interactions. Self-organization process involves formation of two types of patches, majority and…

The dynamical behaviour of a weakly diluted fully-inhibitory network of pulse-coupled spiking neurons is investigated. Upon increasing the coupling strength, a transition from regular to stochastic-like regime is observed. In the…

The paper examines the discrete-time dynamics of neuron models (of excitatory and inhibitory types) with piecewise linear activation functions, which are connected in a network. The properties of a pair of neurons (one excitatory and the…

What dynamical quantity is actually controlled by higher-order interactions in chaotic oscillator networks remains unclear. In amplitude-active systems, chaos is often interpreted through coherence, yet coherence is not the quantity that…

Consistency and predictability of brain functionalities depend on reproducible activity of a single neuron. We identify a reproducible non-chaotic neuronal phase where deviations between concave response latency profiles of a single neuron…

This paper presents a distributed Lyapunov-based control framework for achieving both complete and phase synchronization in a class of leader-follower multi-agent systems composed of identical chaotic agents. The proposed approach…

Reconstructing network dynamics from data is crucial for predicting the changes in the dynamics of complex systems such as neuron networks; however, previous research has shown that the reconstruction is possible under strong constraints…