Related papers: Rhythmic behavior in a two-population mean field I…

We explore the cooperative behaviour and phase transitions of interacting networks by studying a simplified model consisting of Ising spins placed on the nodes of two coupled Erd\"os-R\'enyi random graphs. We derive analytical expressions…

The Ising model on networks plays a fundamental role as a testing ground for understanding cooperative phenomena in complex systems. Here we solve the synchronous dynamics of the Ising model on random graphs with an arbitrary degree…

We study the dynamics of a spin-flip model with a mean field interaction. The system is non reversible, spacially inhomogeneous, and it is designed to model social interactions. We obtain the limiting behavior of the empirical averages in…

To probe the connection between the dynamic phase transition and stochastic resonance, we study the mean-field kinetic Ising model and the two-dimensional Josephson-junction array in the presence of appropriate oscillating magnetic fields.…

Identifying early warning signs of sudden population changes and mechanisms leading to regime shifts are highly desirable in population biology. In this paper, a two-trophic ecosystem comprising of two species of predators, competing for…

In general we are interested in dynamical systems coupled to complex hysteresis. Therefore as a first step we investigated recently the dynamics of a periodically driven damped harmonic oscillator coupled to independent Ising spins in a…

Properties of the two dimensional Ising model with fixed magnetization are deduced from known exact results on the two dimensional Ising model. The existence of a continuous phase transition is shown for arbitrary values of the fixed…

The use of statistical physics to study problems of social sciences is motivated and its current state of the art briefly reviewed, in particular for the case of discrete choice making. The coupling of two binary choices is studied in some…

Asymmetric Ising model, in which coupled spins affect each other differently, plays an important role in diverse fields, from physics to biology to artificial intelligence. We show that coupled parametric oscillators provide a…

We study the spatial patterns formed by a system of interacting particles where the mobility of any individual is determined by the population crowding at two different spatial scales. In this way we model the behavior of some biological…

Critical behavior at an order/disorder phase transition has been a central object of interest in statistical physics. In the past century, techniques borrowed from many different fields of mathematics (Algebra, Combinatorics, Probability,…

The dynamical steady state behaviour of the random field Ising ferromagnet swept by a propagating magnetic field wave is studied at zero temperature by Monte Carlo simulation in two dimensions. The distribution of the random field is…

Microbial populations in the natural environment are likely to experience growth conditions very different from those of a typical laboratory xperiment. In particular, removal rates of biomass and substrate are unlikely to be balanced under…

The phenomena of synchronization and nontrivial collective behavior are studied in a model of coupled chaotic maps with random global coupling. The mean field of the system is coupled to a fraction of elements randomly chosen at any given…

Dynamics of Ising models is a much studied phenomenon and has emerged as a rich field of present-day research. An important dynamical feature commonly studied is the quenching phenomenon below the critical temperature. In this thesis we…

The dynamics of non-equilibrium Ising model with parallel updates is investigated using a generalized mean field approximation that incorporates multiple two-site correlations at any two time steps, which can be obtained recursively. The…

We analyse biased ensembles of trajectories for the random-field Ising model on a fully-connected lattice, which is described exactly by mean-field theory. By coupling the activity of the system to a dynamical biasing field, we find a range…

In many real-world systems, partial synchronization is the dominant dynamical regime and, in systems such as the brain, is often accompanied by collective oscillations in which multiple overlapping modes interact to produce complex rhythmic…

Many real-world systems can be modeled as networks of interacting oscillatory units. Collective dynamics that are of functional relevance for the oscillator network, such as switching between metastable states, arise through the interplay…

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…