ﻻ يوجد ملخص باللغة العربية
We present a nonlinear and non-Markovian random walk model for stochastic movement and the spatial aggregation of living organisms that have the ability to sense population density. We take into account social crowding effects for which the dispersal rate is a decreasing function of the population density and residence time. We perform stochastic simulations of random walk and discover the phenomenon of self-organized anomaly (SOA) which leads to a collapse of stationary aggregation pattern. This anomalous regime is self-organized and arises without the need for a heavy tailed waiting time distribution from the inception. Conditions have been found under which the nonlinear random walk evolves into anomalous state when all particles aggregate inside a tiny domain (anomalous aggregation). We obtain power-law stationary density-dependent survival function and define the critical condition for SOA as the divergence of mean residence time. The role of the initial conditions in different SOA scenarios is discussed. We observe phenomenon of transient anomalous bi-modal aggregation.
Motivated by studies on the recurrent properties of animal and human mobility, we introduce a path-dependent random walk model with long range memory for which not only the mean square displacement (MSD) can be obtained exactly in the asymptotic limi
The motion of self-propelled particles is modeled as a persistent random walk. An analytical framework is developed that allows the derivation of exact expressions for the time evolution of arbitrary moments of the persistent walks displacement. It i
In this paper we have studied a model for self-induced aggregation in Brownian particle incorporating the non-Markovian and non-Gaussian character of the associated random noise process. In this model the time evolution of each individual is guided b
We revisit motility-induced phase separation in two models of active particles interacting by pairwise repulsion. We show that the resulting dense phase contains gas bubbles distributed algebraically up to a typically large cutoff scale. At large eno
Random measurements have been shown to induce a phase transition in an extended quantum system evolving under chaotic unitary dynamics, when the strength of measurements exceeds a threshold value. Below this threshold, a steady state with a sub-therm