Related papers: Anomalous Diffusion and Emergent Universality in C…
Lattice-based random walk models are widely used to study populations of migrating cells with motility bias and proliferation. Crowding is typically represented by volume exclusion, where each lattice site can be occupied by at most one…
The relationship between a driven extended system and an autonomous spatiotemporal system is investigated in the context of coupled map lattice models. Specifically, a locally coupled map lattice subjected to an external drive is compared…
In some systems, the behavior of the constituent units can create a `context' that modifies the direct interactions among them. This mechanism of indirect modification inspired us to develop a minimal model of context-dependent spreading.…
We study the dynamics of long-wavelength fluctuations in one-dimensional (1D) many-particle systems as described by self-consistent mode-coupling theory. The corresponding nonlinear integro-differential equations for the relevant…
We consider discrete dynamical systems of "ant-like" agents engaged in a sequence of pursuits on a graph environment. The agents emerge one by one at equal time intervals from a source vertex $s$ and pursue each other by greedily attempting…
Bias plays an important role in the enhancement of diffusion in periodic potentials. Using the continuous-time random walk in the presence of a bias, we provide a novel mechanism for the enhancement of diffusion in a random energy…
A novel probabilistic framework for modelling anomalous diffusion is presented. The resulting process is Markovian, non-homogeneous, non-stationary, non-ergodic, and state-dependent. The fundamental law governing this process is driven by…
The horizontal dynamics of a bouncing ball interacting with an irregular surface is investigated and is found to demonstrate behavior analogous to a random walk. Its stochastic character is substantiated by the calculation of a permutation…
The question how social norms can emerge from microscopic interactions between individuals is a key problem in social sciences to explain collective behavior. In this paper we propose an agent-based model to show that randomly distributed…
Uncovering the mechanism behind the scaling law in human trajectories is of fundamental significance in understanding many spatio-temporal phenomena. In combination of the exploration and the preferential returns, we propose a simple…
In search for mathematically tractable models of anomalous diffusion, we introduce a simple dynamical system consisting of a chain of coupled maps of the interval whose Lyapunov exponents vanish everywhere. The volume preserving property…
Understanding the interplay between human behavioral phenomena and infectious disease dynamics has been one of the central challenges of mathematical epidemiology. However, socio-cognitive processes critical for the initiation of desired…
The problem of sums of independent, identically distributed random variables with stretched-exponential tails exhibits a dynamical phase transition and has recently reemerged in the context of active transport and condensation phenomena. We…
In this paper, we conduct a literature review of laws of motion based on stochastic search strategies which are mainly focused on exploring highly dynamic environments. In this regard, stochastic search strategies represent an interesting…
Community assembly is studied using individual-based multispecies models. The models have stochastic population dynamics with mutation, migration, and extinction of species. Mutants appear as a result of mutation of the resident species,…
Patterns of avoidance, adjacency, and association in complex systems design emerge from the system's underlying logical architecture (functional relationships among components) and physical architecture (component physical properties and…
Complex networks have been found to provide a good representation of the structure of knowledge, as understood in terms of discoverable concepts and their relationships. In this context, the discovery process can be modeled as agents…
Random walks are ubiquitous in the sciences, and they are interesting from both theoretical and practical perspectives. They are one of the most fundamental types of stochastic processes; can be used to model numerous phenomena, including…
We study the causes of anomalous dispersion in Darcy-scale porous media characterized by spatially heterogeneous hydraulic properties. Spatial variability in hydraulic conductivity leads to spatial variability in the flow properties through…
We study the collective motion of autonomous mobile agents on a ringlike environment. The agents' dynamics is inspired by known laboratory experiments on the dynamics of locust swarms. In these experiments, locusts placed at arbitrary…