Related papers: Competing deterministic growth models in two dimen…
In a recent paper [arXiv:1506.06649 [nlin.CG]], we presented an example of a 3-state cellular automaton which exhibits behaviour analogous to degenerate hyperbolicity often observed in finite-dimensional dynamical systems. We also…
In this paper we study the dynamics of 1- and 2- dimensional cellular automata, using a 2-adic representation of the states, we give a simple graphical technique for finding periodic solutions. We also study the continuity properties of the…
We stress that in contradiction with what happens in space dimensions $n \geq 3$, there is no strict bound on the number of bound states with the same structure as the semi-classical estimate for large coupling constant and give, in two…
The spatial arrangement of individuals is thought to overcome the dilemma of cooperation: When cooperators engage in clusters they might share the benefit of cooperation while being more protected against non-cooperating individuals, which…
We integrate dual-process theories of human cognition with evolutionary game theory to study the evolution of automatic and controlled decision-making processes. We introduce a model where agents who make decisions using either automatic or…
The dynamics of linear stochastic growth equations on growing substrates is studied. The substrate is assumed to grow in time following the power law $t^\gamma$, where the growth index $\gamma$ is an arbitrary positive number. Two different…
We study competition of two spreading colors starting from single sources on the configuration model with i.i.d. degrees following a power-law distribution with exponent tau in (2,3). In this model two colors spread with a fixed but not…
Dynamics maintaining diversity of cell types in a multi-cellular system are studied in relationship with the plasticity of cellular states. By adopting a simple theoretical framework for intra-cellular chemical reaction dynamics with…
In this paper we study the emergence of homeostasis in a two-layer system of the Game of Life, in which the Game of Life in the first layer couples with another system of cellular automata in the second layer. Homeostasis is defined here as…
We consider a model of adversarial dynamics consisting of three populations, labelled Blue, Green and Red, which evolve under a system of first order nonlinear differential equations. Red and Blue populations are adversaries and interact…
We study several deterministic one-dimensional traffic models. For integer positions and velocities we find the typical high and low density phases separated by a simple transition. If positions and velocities are continuous variables the…
We study the spatial distributions of two randomly interacting species, in the presence of an external multiplicative colored noise. The dynamics of the ecosystem is described by a coupled map lattice model. We find a nonmonotonic behavior…
A general criterion for the existence of phase separation in driven one-dimensional systems is proposed. It is suggested that phase separation is related to the size dependence of the steady-state currents of domains in the system. A…
We consider a one-dimensional model consisting of an assembly of two-velocity particles moving freely between collisions. When two particles meet, they instantaneously annihilate each other and disappear from the system. Moreover each…
This paper is concerned with reaction-diffusion systems of two symmetric species in spatial dimension one, having two stable symmetric equilibria connected by a symmetric standing front. The first order variation of the speed of this front…
We study and compare the time evolutions of concurrence and quantum discord in a driven system of two interacting qubits prepared in a generic Werner state. The~corresponding quantum dynamics is exactly treated and manifests the appearance…
We study a one-dimensional, nonequilibrium Potts-like model which has $q$ symmetric absorbing states. For $q=2$, as expected, the model belongs to the parity conserving universality class. For $q=3$ the critical behaviour depends on the…
We study the dynamical properties of the ordered phases obtained in a coupled nonequilibrium system describing advection of two species of particles by a stochastically evolving landscape. The local dynamics of the landscape also gets…
High dimensional dynamics play a vital role in brain function, ecological systems, and neuro-inspired machine learning. Where and how these dynamics are confined in the phase space remains challenging to solve. Here, we provide an analytic…
One-directional traffic on two-lanes is modeled in the framework of a spring-block type model. A fraction $q$ of the cars are allowed to change lanes, following simple dynamical rules, while the other cars keep their initial lane. The…