相关论文: Random replicators with asymmetric couplings
We study analytically the performance of a recently proposed algorithm for learning the couplings of a random asymmetric kinetic Ising model from finite length trajectories of the spin dynamics. Our analysis shows the importance of the…
Stochastic reaction networks are mathematical models with a wide range of applications in biochemistry, ecology, and epidemiology, and are often complex to analyze. Except for some special cases, it is generally difficult to predict how the…
Non-autonomous perturbations of isochronous systems in the plane are considered. It is assumed that the intensity of perturbations decays with time, and the frequency is asymptotically constant with the limiting value satisfying a resonance…
We investigate the renormalization group flows and fixed point structure of many coupled minimal models. The models are coupled two by two by energy-energy couplings. We take the general approach where the bare couplings are all taken to be…
We investigate the dynamics of a two-dimensional array of oscillators with phase-shifted coupling. Each oscillator is allowed to interact with its neighbors within a finite radius. The system exhibits various patterns including squarelike…
We characterize synchronization phenomenon in discrete-time, discrete-state random dynamical systems, with random and probabilistic Boolean networks as particular examples. In terms of multiplicative ergodic properties of the induced linear…
We consider the pattern formation problem in coupled identical systems after the global synchronized state becomes unstable. Based on analytical results relating the coupling strengths and the instability of each spatial mode (pattern) we…
The synchronous dynamics and the stationary states of a recurrent attractor neural network model with competing synapses between symmetric sequence processing and Hebbian pattern reconstruction is studied in this work allowing for the…
We consider systems of many spatially distributed phase oscillators that interact with their neighbors. Each oscillator is allowed to have a different natural frequency, as well as a different response time to the signals it receives from…
The thermodynamic framework of repeated interactions is generalized to an arbitrary open quantum system in contact with a heat bath. Based on these findings the theory is then extended to arbitrary measurements performed on the system. This…
The theory of phase transitions is based on the consideration of "idealized" models, such as the Ising model: a system of magnetic moments living on a cubic lattice and having only two accessible states. For simplicity the interaction is…
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…
The effect of interactions on a system of fermions that are in a non-equilibrium steady state due to a quantum quench is studied employing the random-phase-approximation (RPA). As a result of the quench, the distribution function of the…
The replicator equation is ubiquitous for many areas of mathematical biology. One of major shortcomings of this equation is that it does not allow for an explicit spatial structure. Here we review analytical approaches to include spatial…
We establish the existence of two weak coupling regime effective dynamics for an open quantum system of repeated interactions (vanishing strength and individual interaction duration, respectively). This generalizes known results in that the…
A minimalistic model of the half-center oscillator is proposed. Within it, we consider dynamics of two excitable neurons interacting by means of the excitatory coupling. In the parameter space of the model, we identify the regions of…
The study of synchronization in populations of coupled biological oscillators is fundamental to many areas of biology to include neuroscience, cardiac dynamics and circadian rhythms. Studying these systems may involve tracking the…
The dynamics of patterns in large two-dimensional domains remains a challenge in non-equilibrium phenomena. Often it is addressed through mild extensions of one-dimensional equations. We show that full 2D generalizations of the latter can…
We revisit the replica method for analyzing inference and learning in parametric models, considering situations where the data-generating distribution is unknown or analytically intractable. Instead of assuming idealized distributions to…
We discuss 2D systems with Ising symmetry and competing interactions at different scales. In the framework of the Renormalization Group, we study the effect of relevant quartic interactions. In addition to the usual constant interaction…