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Random Boolean networks, originally invented as models of genetic regulatory networks, are simple models for a broad class of complex systems that show rich dynamical structures. From a biological perspective, the most interesting networks…
What is the reason for complex dynamical patterns registered from real biological neuronal networks? Noise and dynamical reconfiguring of a network (functional/dynamic connectome) were proposed as possible answers. In this case study, we…
Recurrence in the phase space of complex systems is a well-studied phenomenon, which has provided deep insights into the nonlinear dynamics of such systems. For dissipative systems, characteristics based on recurrence plots have recently…
We present and discuss the results of an experimental analysis in the design of Boolean networks by means of genetic algorithms. A population of networks is evolved with the aim of finding a network such that the attractor it reaches is of…
New chaos-based communication schemes for transmission of analog and digital information are suggested. The carrier signal is produced by chaotic generator having well-defined oscillation phases at least on short time intervals. For data…
Discovery of causal relations is fundamental for understanding the dynamics of complex systems. While causal interactions are well defined for acyclic systems that can be separated into causally effective subsystems, a mathematical…
This paper shows that a large class of fading memory state-space systems driven by discrete-time observations of dynamical systems defined on compact manifolds always yields continuously differentiable synchronizations. This general result…
This paper studies the mathematical properties of collectively canalizing Boolean functions, a class of functions that has arisen from applications in systems biology. Boolean networks are an increasingly popular modeling framework for…
We describe systems using Kauffman and similar networks. They are directed funct ioning networks consisting of finite number of nodes with finite number of discr ete states evaluated in synchronous mode of discrete time. In this paper we…
Many practical systems can be described by dynamic networks, for which modern technique can measure their output signals, and accumulate extremely rich data. Nevertheless, the network structures producing these data are often deeply hidden…
It has been demonstrated earlier that universal computation is 'almost surely' chaotic. Machine learning is a form of computational fixed point iteration, iterating over the computable function space. We showcase some properties of this…
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…
In the present study, we investigate the dynamics of impulsive differential equations driven by a chaotic system. We rigorously prove that, likewise the drive, the response impulsive system is also chaotic. Our results are based on the…
Due to the deterministic nature of chaotic systems, fluctuations in their trajectories arise solely from the choice of initial conditions. Some of these dynamical fluctuations may lead to extremely unlikely scenarios. Understanding the…
In this paper the chaotic properties of the TCP congestion avoidance mechanism are investigated. The analysis focuses on the origin of the complex behavior appearing in deterministic TCP/IP networks. From the traffic modeling point of view…
We present a new optoelectronic architecture intended for chaotic optical intensity generation. The principle relies on an electro-optic non-linear delay dynamics, which non linearity is performed by a 4-waves integrated optics…
Chaos is omnipresent in nature, and its understanding provides enormous social and economic benefits. However, the unpredictability of chaotic systems is a textbook concept due to their sensitivity to initial conditions, aperiodic behavior,…
We study nonautonomous discrete dynamical systems with randomly perturbed trajectories. We suppose that such a system is generated by a sequence of continuous maps which converges uniformly to a map $f$. We give conditions, under which a…
We show that the output of systems with time-varying delay can exhibit a new kind of chaotic behavior characterized by laminar phases, which are periodically interrupted by irregular bursts. Within each laminar phase the output intensity…
We discuss how to characterize the behavior of a chaotic dynamical system depending on a parameter that varies periodically in time. In particular, we study the predictability time, the correlations and the mean responses, by defining a…