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This article considers the computational (acoustic) wave propagation in strongly heterogeneous structures beyond the assumption of periodicity. A high contrast between the constituents of microstructured multiphase materials can lead to…
We investigate energy propagation in a one-dimensional stub lattice in the presence of both disorder and nonlinearity. In the periodic case, the stub lattice hosts two dispersive bands separated by a flat band; however, we show that…
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…
Despite their apparent simplicity, random Boolean networks display a rich variety of dynamical behaviors. Much work has been focused on the properties and abundance of attractors. We here derive an expression for the number of attractors in…
We determine the propagation properties of a quantum particle in a d-dimensional lattice with hopping disorder, delta-correlated in time. The system is delocalized: the averaged transition probability shows a diffusive behavior. Then,…
The deterministic dynamics of randomly connected neural networks are studied, where a state of binary neurons evolves according to a discreet-time synchronous update rule. We give a theoretical support that the overlap of systems' states…
In a communication scheme, there exist points at the transmitter and at the receiver where the wave is reduced to a finite set of functions of time which describe amplitudes and phases. For instance, the information is summarized in…
We study the properties of mode-mode interactions for waves propagating in nonlinear disordered one-dimensional systems. We focus on i) the localization volume of a mode which defines the number of interacting partner modes, ii) the overlap…
The density stratification in an incompressible fluid is responsible for the propagation of internal waves. In domains with topography, these waves exhibit interesting features. In particular, numerical and lab experiments show that, in two…
We study numerically the transport and localization properties of waves in ordered and disordered ladder-shaped lattices with local $\mathcal{PT}$ symmetry. Using a transfer matrix method, we calculate the transmittance and the reflectance…
Diffusion processes are instrumental to describe the movement of a continuous quantity in a generic network of interacting agents. Here, we present a probabilistic framework for diffusion in networks and propose to classify agent…
The propagation of a continuous wave in the average anomalous dispersion region of a dispersion oscillating fiber is investigated numerically and experimentally. We demonstrate that the train of solitons arising from modulation instability…
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…
A new method of path averaging for waves propagating in a random dilute system of identical scatterers is developed. The scattering matrix of such a system is calculated. The method systematically takes into account repeating scatterings on…
Due to the regularization effect of the stochastic noise, the quantitative entropy-cost type propagation of chaos for mean field interacting particle system is proposed. The result shows that the Kac's chaotic property measured in relative…
We study the properties of the distance between attractors in Random Boolean Networks, a prominent model of genetic regulatory networks. We define three distance measures, upon which attractor distance matrices are constructed and their…
In various situations where wave transport is preeminent, like in wireless communication, a strong established transmission is present in a complex scattering environment. We develop a novel approach to describe emerging fluctuations, which…
Spreading phenomena essentially underlie the dynamics of various natural and technological networked systems, yet how spatiotemporal propagation patterns emerge from such networks remains largely unknown. Here we propose a novel approach…
It has been proposed to make practical use of chaos in communication, in enhancing mixing in chemical processes and in spreading the spectrum of switch-mode power suppies to avoid electromagnetic interference. It is however known that for…
Random walks serve as important tools for studying complex network structures, yet their dynamics in cases where transition probabilities are not static remain under explored and poorly understood. Here we study nonlinear random walks that…