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(Bi)multi-partite interaction patterns are commonly observed in real world systems which have inhibitory and excitatory couplings. We hypothesize these structural interaction pattern to be stable and naturally arising in the course of…
We construct and investigate Boolean networks that follow a given reliable trajectory in state space, which is insensitive to fluctuations in the updating schedule, and which is also robust against noise. Robustness is quantified as the…
In this paper we study the dynamics of nonlinear random walks. While typical random walks on networks consist of standard Markov chains whose static transition probabilities dictate the flow of random walkers through the network, nonlinear…
Emerging collective behavior in complex dynamical networks depends on both coupling function and underlying coupling topology. Through this perspective, we provide a brief yet profound excerpt of recent research efforts that explore how the…
Introduction: Machine learning provides fundamental tools both for scientific research and for the development of technologies with significant impact on society. It provides methods that facilitate the discovery of regularities in data and…
The Kauffman model describes a system of randomly connected nodes with dynamics based on Boolean update functions. Though it is a simple model, it exhibits very complex behavior for "critical" parameter values at the boundary between a…
A succesful method to describe the asymptotic behavior of a discrete time stochastic process governed by some recursive formula is to relate it to the limit sets of a well chosen mean differential equation. Under an attainability condition,…
We extend a recently introduced class of exactly solvable models for recurrent neural networks with competition between 1D nearest neighbour and infinite range information processing. We increase the potential for further frustration and…
The behaviour of many real-world phenomena can be modelled by nonlinear dynamical systems whereby a latent system state is observed through a filter. We are interested in interacting subsystems of this form, which we model by a set of…
We studied, both analytically and numerically, complex excitable networks, in which connections are time dependent and some of the nodes remain silent at each time step. More specifically, (a) there is a heterogenous distribution of…
We investigate a model of evolving random network, introduced by us previously {[}{\it Phys. Rev. Lett.} {\bf 83}, 5587 (1999){]} . The model is a generalization of the Bak-Sneppen model of biological evolution, with the modification that…
Systems with many stable configurations abound in nature, both in living and inanimate matter. Their inherent nonlinearity and sensitivity to small perturbations make them challenging to study, particularly in the presence of external…
A key question in brain sciences is how to identify time-evolving functional connectivity, such as that obtained from recordings of neuronal activity over time. We wish to explain the observed phenomena in terms of latent states which, in…
Using analytic arguments, we show that dynamical attractor periods in large critical Boolean networks are power-law distributed. Our arguments are based on the method of relevant components, which focuses on the behavior of the nodes that…
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…
Competitive interactions represent one of the driving forces behind evolution and natural selection in biological and sociological systems. For example, animals in an ecosystem may vie for food or mates; in a market economy, firms may…
We investigate the predictive power of recurrent neural networks for oscillatory systems not only on the attractor, but in its vicinity as well. For this we consider systems perturbed by an external force. This allows us to not merely…
We study the stochastic dynamics of a system of interacting species in a stochastic environment by means of a continuous-time Markov chain with transition rates depending on the state of the environment. Models of gene regulation in systems…
We consider continuous time Hopfield-like recurrent networks as dynamical models for gene regulation and neural networks. We are interested in networks that contain n high-degree nodes preferably connected to a large number of Ns weakly…
In this paper, we model a decision-making process involving a set of interacting agents. We use Markovian opinion dynamics, where each agent switches between decisions according to a continuous time Markov chain. Existing opinion dynamics…