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Mathematical models of interacting populations are often constructed as systems of differential equations, which describe how populations change with time. Below we study one such model connected to the nonlinear dynamics of a system of…
The late-stage phase ordering, in $d=2$ dimensions, of symmetric fluid mixtures violates dynamical scaling. We show however that, even at 50/50 volume fractions, if an asymmetric droplet morphology is initially present then this sustains…
We investigate the dynamic behavior of finite-size systems close to a first-order transition (FOT). We develop a dynamic finite-size scaling (DFSS) theory for the dynamic behavior in the coexistence region where different phases coexist. It…
This paper studies a consensus problem in multidimensional networks having the same agent-to-agent interaction pattern under both intra- and cross-layer time delays. Several conditions for the agents to asymptotically reach a consensus are…
We show how a variety of stable spatio-temporal periodic patterns can be created in 2D-lattices of coupled oscillators with non-homogeneous coupling delays. A "hybrid dispersion relation" is introduced, which allows studying the stability…
Random walks describe diffusion processes, where movement at every time step is restricted to only the neighbouring locations. We construct a quantum random walk algorithm, based on discretisation of the Dirac evolution operator inspired by…
The voter model is a paradigm of ordering dynamics. At each time step, a random node is selected and copies the state of one of its neighbors. Traditionally, this state has been considered as a binary variable. Here, we relax this…
We show that the vertex-reinforced jump process on the $d$-dimensional lattice with long-range jumps is transient in any dimension $d$ as long as the initial weights do not decay too fast. The main ingredients in the proof are: an analysis…
In this paper, a new framework for crossover of scaling law is proposed: a crossover of scaling law can be described by a self-similar solution. A crossover emerges as a result of the interference from similarity parameters of the higher…
A nonlinear time-delay model is proposed to describe the interaction dynamics between criminal and non-criminal populations, combining social influence mechanisms, saturation effects represented by a Holling type II functional response, and…
The vibro-impact capsule system is a self-propelled mechanism that has abundant coexisting attractors and moves rectilinearly under periodic excitation when overcoming environmental resistance. In this paper, we study the control of…
We investigate the dynamics of a single tracer particle performing Brownian motion in a two-dimensional course of randomly distributed hard obstacles. At a certain critical obstacle density, the motion of the tracer becomes anomalous over…
We have studied numerically the random interchange model and related loop models on the three-dimensional cubic lattice. We have determined the transition time for the occurrence of long loops. The joint distribution of the lengths of long…
We consider a self-attracting random walk in dimension d=1, in presence of a field of strength s, which biases the walker toward a target site. We focus on the dynamic case (true reinforced random walk), where memory effects are implemented…
The random walk process underlies the description of a large number of real world phenomena. Here we provide the study of random walk processes in time varying networks in the regime of time-scale mixing; i.e. when the network connectivity…
Recent analysis of social communications among humans has revealed that the interval between interactions for a pair of individuals and for an individual often follows a long-tail distribution. We investigate the effect of such a…
We study the voter model and related random-copying processes on arbitrarily complex network structures. Through a representation of the dynamics as a particle reaction process, we show that a quantity measuring the degree of order in a…
Feedback control plays a central role in active matter, yet it is inevitably accompanied by noise and finite perception--action delays. This Perspective reviews recent advances on active systems with delayed interactions, showing how time…
We use a one-dimensional random walk on $D$-dimensional hyper-spheres to determine the critical behavior of statistical systems in hyper-spherical geometries. First, we demonstrate the properties of such walk by studying the phase diagram…
Delay or queue length information has the potential to influence the decision of a customer to use a service system. Thus, it is imperative for service system managers to understand how the information that they provide will affect the…