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We investigate a simplified model of two fully connected magnetic systems maintained at different temperatures by virtue of being connected to two independent thermal baths while simultaneously being inter-connected with each other. Using…
Synchronization is one of the paradigmatic phenomena in the study of complex systems. It has been explored theoretically and experimentally mostly to understand natural phenomena, but also in view of technological applications. Although…
The quantum dynamics of isolated systems under quench condition exhibits a variety of interesting features depending on the integrable/chaotic nature of system. We study the exact dynamics of trivially integrable system of harmonic chains…
In this contribution we give an overview over recent work on the theory of interacting neural networks. The model is defined in Section 2. The typical teacher/student scenario is considered in Section 3. A static teacher network is…
We study synaptically coupled neuronal networks to identify the role of coupling delays in network's synchronized behaviors. We consider a network of excitable, relaxation oscillator neurons where two distinct populations, one excitatory…
We consider a distributed stochastic optimization problem in networks with finite number of nodes. Each node adjusts its action to optimize the global utility of the network, which is defined as the sum of local utilities of all nodes.…
Coherent, large scale dynamics in many nonequilibrium physical, biological, or information transport networks are driven by small-scale local energy input. Here, we introduce and explore an analytically tractable nonlinear model for…
In this work we investigate heat conduction along a ladder-model conformed by two coupled one dimensional lattices with different anharmonicity. We study how the interchain coupling modifies the thermal properties of the isolated systems.…
We consider networks of massive particles connected by non-linear springs. Some particles interact with heat baths at different temperatures, which are modeled as stochastic driving forces. The structure of the network is arbitrary, but the…
We study a one-dimensional hamiltonian chain of masses perturbed by an energy conserving noise. The dynamics is such that, according to its hamiltonian part, particles move freely in cells and interact with their neighbors through…
We reply to the recent note "Comment on Synchronization dynamics in non-normal networks: the trade-off for optimality", showing that the authors base their claims mainly on general theoretical arguments that do not necessarily invalidate…
A model is investigated where a monochromatic, spatially homogeneous laser field interacts with an electron in a one-dimensional periodic lattice. The classical Hamiltonian is presented and the technique of stroboscopic maps is used to…
We present a study of exclusion process on a peculiar topology of network with two intersected lanes, competing for the particles in a reservoir with finite capacity. To provide a theoretical ground for our findings, we exploit mean-field…
Stability of power networks is an increasingly important topic because of the high penetration of renewable distributed generation units. This requires the development of advanced (typically model-based) techniques for the analysis and…
We consider a one-dimensional mono-atomic lattice with random perturbations of masses spread over a finite number of particles. Assuming Newtonian dynamics and linear nearest-neighbour interactions and allowing for a provision of pinning…
In this work we investigate time varying networks with complex dynamics at the nodes. We consider two scenarios of network change in an interval of time: first, we have the case where each link can change with probability pt, i.e. the…
We propose an exactly soluble W*-dynamical system generated by repeated harmonic perturbations of the one-mode quantum oscillator. In the present paper we deal with the case of isolated system. Although dynamics is Hamiltonian and…
Based on a rigorous extension of classical statistical mechanics to networks, we study a specific microscopic network Hamiltonian. The form of this Hamiltonian is derived from the assumption that individual nodes increase/decrease their…
A simple model of wave-particle interaction is studied in its self-consistent form, that is, where the particles are allowed to feedback on the waves dynamics. We focus on the configurations of locked solutions (equilibria) and how the…
We address the problem of simulating pair-interaction Hamiltonians in n node quantum networks where the subsystems have arbitrary, possibly different, dimensions. We show that any pair-interaction can be used to simulate any other by…