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The dynamical evolution of dislocations in plastically deformed metals is controlled by both deterministic factors arising out of applied loads and stochastic effects appearing due to fluctuations of internal stress. Such type of stochastic…
We consider a general swarm model of self-propelling agents interacting through a pairwise potential in the presence of noise and communication time delay. Previous work [Phys. Rev. E 77, 035203(R) (2008)] has shown that a communication…
Intracellular transport processes are essential to the healthy development of many organisms as well as more generally to healthy cellular function. The complex dynamics and interactions between protein molecules and filaments on different…
We study how environmental stochasticity influences the long-term population size in certain one- and two-species models. The difficulty is that even when one can prove that there is persistence, it is usually impossible to say anything…
Correlated fluctuations in the activity of neural populations reflect the network's dynamics and connectivity. The temporal and spatial dimensions of neural correlations are interdependent. However, prior theoretical work mainly analyzed…
System-environment interactions are intrinsically nonlinear and dependent on the interplay between many degrees of freedom. The complexity may be even more pronounced when one aims to describe biologically motivated systems. In that case,…
We investigate how environmental flows influence spatial pattern formation and population dynamics using two nonlocal models of population dynamics, which we couple to two different stationary flows. Combining numerical simulations and…
In this paper we present a general framework in which one can rigorously study the effect of spatio-temporal noise on traveling waves, stationary patterns and oscillations that are invariant under the action of a finite-dimensional set of…
We analyze the effects of additive, spatially extended noise on spatiotemporal patterns in continuum neural fields. Our main focus is how fluctuations impact patterns when they are weakly coupled to an external stimulus or another…
Based on previously published experimental observations and mathematical models for Hes1, p53 and NF-kB gene expression, we improve these models through a distributed delay formulation of the time lag between transcription factor binding…
This chapter provides a pedagogical introduction and overview of spatial and temporal correlation and fluctuation effects resulting from the fundamentally stochastic kinetics underlying chemical reactions and the dynamics of populations or…
Background: Mechanotransduction in bone cells plays a pivotal role in osteoblast differentiation and bone remodelling. Mechanotransduction provides the link between modulation of the extracellular matrix and intracellular actions. By…
The dynamics of an ensemble of bistable elements with global time-delayed coupling under the influence of noise is studied analytically and numerically. Depending on the noise level the system undergoes ordering transitions and demonstrates…
We study the effects of demographic stochasticity on the long-term dynamics of biological coevolution models of community assembly. The noise is induced in order to check the validity of deterministic population dynamics. While mutualistic…
Spatio-temporal patterns emerging from an initial quiescent, uniform state is a phenomenon observed in many dynamical systems sustained far from thermodynamic equilibrium, the practical application of which has only recently begun to be…
The result of 2-dimensional Gaussian lattice fit to a speckle intensity pattern based on a linear model that includes nearest-neighbor interactions is presented. We also include a Monte Carlo simulation of the same spatial speckle pattern…
In this article, we quantitatively study, through stochastic models, the efects of several intracellular phenomena, such as cell volume growth, cell division, gene replication as well as fuctuations of available RNA polymerases and…
We investigate the behavior of the residence times density function for different nonlinear dynamical systems with limit cycle behavior and perturbed parametrically with a colored noise. We present evidence that underlying the stochastic…
The effects of demographic stochasticity in the long term behaviour of endemic infectious diseases have been considered for long as a necessary addition to an underlying deterministic theory. The latter would explain the regular behaviour…
Based on symmetry consideration of migration and shape deformations, we formulate phenomenologically the dynamics of cell crawling in two dimensions. Forces are introduced to change the cell shape. The shape deformations induce migration of…