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The dynamical behavior of networked systems is expected to reflect the features of their coupling structure. Yet, symmetry-broken solutions often occur in symmetrically coupled networks. An example is provided by the so-called solitary…
Neuronal networks constitute a special class of dynamical systems, as they are formed by individual geometrical components, namely the neurons. In the existing literature, relatively little attention has been given to the influence of…
The dynamics of an ensemble of bistable elements with global time-delayed coupling under the influence of noise is studied analytically and numerically. Depending on the noise level the system undergoes ordering transitions and demonstrates…
We study the evolution of a random weighted network with complex nonlinear dynamics at each node, whose activity may cease as a result of interactions with other nodes. Starting from a knowledge of the micro-level behaviour at each node, we…
The identification of the limiting factors in the dynamical behavior of complex systems is an important interdisciplinary problem which often can be traced to the spectral properties of an underlying network. By deriving a general relation…
Chaotic strings are particular classes of coupled map lattices that can serve as models for vacuum fluctuations in stochastically quantized field theories. They have been previously shown to distinguish standard model coupling parameters as…
Phase-transitionlike behavior is found to occur in globally coupled systems of finite number of elements, and its theoretical explanation is provided. The system studied is a population of globally pulse-coupled integrate-and-fire cells…
The control of complex networks is of paramount importance in areas as diverse as ecosystem management, emergency response, and cell reprogramming. A fundamental property of networks is that perturbations to one node can affect other nodes,…
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 the spatial distributions of two randomly interacting species, in the presence of an external multiplicative colored noise. The dynamics of the ecosystem is described by a coupled map lattice model. We find a nonmonotonic behavior…
The observed long-range spatiotemporal correlations of real world dynamical systems is governed by quantumlike mechanics with inherent non-local connections. In summary, microscopic scale local fluctuations form a unified self-organized…
We study the dynamical states that emerge in a small-world network of recurrently coupled excitable neurons through both numerical and analytical methods. These dynamics depend in large part on the fraction of long-range connections or…
Structure entails function and thus a structural description of the brain will help to understand its function and may provide insights into many properties of brain systems, from their robustness and recovery from damage, to their dynamics…
Large populations of globally-coupled identical maps subjected to independent additive noise are shown to undergo qualitative changes as the features of the stochastic process are varied. We show that for strong coupling, the collective…
Collective behavior in large ensembles of dynamical units with non-pairwise interactions may play an important role in several systems ranging from brain function to social networks. Despite recent work pointing to simplicial structure,…
The study of the interplay between the structure and dynamics of complex multilevel systems is a pressing challenge nowadays. In this paper, we use a semi-annealed approximation to study the stability properties of Random Boolean Networks…
We consider synchronization of chaotic systems coupled indirectly through a common environmnet where the environment has an intrinsic dynmics of its own modulated via feedback from the systems. We find that a rich vareity of synchronization…
Continuous-time systems with switch-like behaviour occur in chemical kinetics, gene regulatory networks and neural networks. Networks with hard switching, as a limiting case of smooth sigmoidal switching, retain the richest possible range…
We quantify the finite size effects in a stochastic network made up of rate neurons, for several kinds of recurrent connectivity matrices. This analysis is performed by means of a perturbative expansion of the neural equations, where the…
As a model of temporally evolving networks, we consider a globally coupled logistic map with variable connection weights. The model exhibits self-organization of network structure, reflected by the collective behavior of units. Structural…