Related papers: Phase transition for a contact process with random…
In a physical system, changing parameters such as temperature can induce a phase transition: an abrupt change from one state of matter to another. Analogous phenomena have recently been observed in large language models. Typically, the task…
We consider a spatial stochastic model for a pathogen population growing inside a host that attempts to eliminate the pathogens through its immune system. The pathogen population is divided into different types. A pathogen can either…
We study the problem of phase separation in systems with a positive definite order parameter, and in particular, in systems with absorbing states. Owing to the presence of a single minimum in the free energy driving the relaxation kinetics,…
The transient behavior of an ecosystem with N random interacting species in the presence of a multiplicative noise is analyzed. The multiplicative noise mimics the interaction with the environment. We investigate different asymptotic…
We consider the contact process on a dynamic graph defined as a random $d$-regular graph with a stationary edge-switching dynamics. In this graph dynamics, independently of the contact process state, each pair $\{e_1,e_2\}$ of edges of the…
In this paper, we introduce a family of processes with values on the nonnegative integers that describes the dynamics of populations where individuals are allowed to have different types of interactions. The types of interactions that we…
To mimic the complex transport-like collective phenomena in a man-made or natural system, we study an open network junction model of totally asymmetric simple exclusion process with bulk particle attachment and detachment. The stationary…
We study a non-conserved one-dimensional stochastic process which involves two species of particles $A$ and $B$. The particles diffuse asymmetrically and react in pairs as $A\emptyset\leftrightarrow AA\leftrightarrow BA \leftrightarrow…
We introduce an analytical model for population dynamics with intra-specific competition, mutation and assortative mating as basic ingredients. The set of equations that describes the time evolution of population size in a mean-field…
We have numerically studied the trapping problem in a two-dimensional lattice where particles are continuously generated. We have introduced interaction between particles and directionality of their movement. This model presents a critical…
In this paper, we consider the relationship between phase-type distributions and positive systems through practical examples. Phase-type distributions, commonly used in modelling dynamic systems, represent the temporal evolution of a set of…
Interactions often require the proximity between particles. The movement of particles, thus, drives the change of the neighbors which are located in their proximity, leading to a sequence of interactions. In pathogenic contagion, infections…
Dynamic processes in complex networks are crucial for better understanding collective behavior in human societies, biological systems, and the internet. In this paper, we first focus on the continuous Markov-based modeling of evolving…
Density dependence is important in the ecology and evolution of microbial and cancer cells. Typically, we can only measure net growth rates, but the underlying density-dependent mechanisms that give rise to the observed dynamics can…
We present a model for host-parasite dynamics which incorporates both vertical and horizontal transmission as well as spatial structure. Our model consists of stacked contact processes (CP), where the dynamics of the host is a simple CP on…
It is known that the limiting behavior of the contact process strongly depends upon the geometry of the graph on which particles evolve: while the contact process on the regular lattice exhibits only two phases, the process on homogeneous…
An organism that is newly introduced into an existing population has a survival probability that is dependent on both the population density of its environment and the competition it experiences with the members of that population.…
We study a system of self-propelled disks that perform run-and-tumble motion, where particles can adopt more than one internal state. One of those internal states can be transmitted to another particle if the particle carrying this state…
We explain the principles of gene expression pattern stabilization in systems of interacting, diffusible morphogens, with dynamically established source regions. Using a reaction-diffusion model with step-function production term, we…
An effective Hamiltonian describing interaction between generic "fast" and a "slow" systems is obtained in the strong interaction limit. The result is applied for studying the effect of quantum phase transition as a bifurcation of the…