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Fine-grain patterns produced by juxtacrine signalling, have been studied using static monolayers as cellular domains. Unfortunately, analytical results are restricted to a few cells due to the algebraic complexity of nonlinear dynamical…

Motivated by uncertainty quantification in natural transport systems, we investigate an individual-based transport process involving particles undergoing a random walk along a line of point sinks whose strengths are themselves independent…

We propose a stochastic dynamical model of noisy neural networks with complex architectures and discuss activation of neural networks by a stimulus, pacemakers and spontaneous activity. This model has a complex phase diagram with…

We present a path integral formalism to compute potentials for nonequilibrium steady states, reached by a multiplicative stochastic dynamics. We develop a weak-noise expansion, which allows the explicit evaluation of the potential in…

This work is concerned with existence of weak solutions to discon- tinuous stochastic differential equations driven by multiplicative Gaus- sian noise and sliding mode control dynamics generated by stochastic differential equations with…

In the cerebral cortex, neurons are subject to a continuous bombardment of synaptic inputs originating from the network's background activity. This leads to ongoing, mostly subthreshold membrane dynamics that depends on the statistics of…

Timing is essential for many cellular processes, from cellular responses to external stimuli to the cell cycle and circadian clocks. Many of these processes are based on gene expression. For example, an activated gene may be required to…

We have studied sidebranching induced by fluctuations in dendritic growth. The amplitude of sidebranching induced by internal (equilibrium) concentration fluctuations in the case of solidification with solutal diffusion is computed. This…

This paper explores a stochastic Gause predator-prey model with bounded or sub-linear functional response. The model, described by a system of stochastic differential equations, captures the influence of stochastic fluctuations on…

In this paper, we study the limiting behavior for stochastic differential equations driven by non-Gaussian alpha-stable Levy noise as alpha approaches 2. We first prove the convergence of solutions for system driven by alpha-stable Levy…

A variety of living and non-living systems exhibit collective motion. From swarm robotics to bacterial swarms, and tissue wound healing to human crowds, examples of collective motion are highly diverse but all of them share the common…

Motivated by a stochastic differential equation describing the dynamics of interfaces, we study the bifurcation behavior of a more general class of such equations. These equations are characterized by a 2-dimensional phase space (describing…

Modeling stochasticity in gene regulatory networks is an important and complex problem in molecular systems biology. To elucidate intrinsic noise, several modeling strategies such as the Gillespie algorithm have been used successfully. This…

We present a simple analytical tool which gives an approximate insight into the stationary behavior of nonlinear systems undergoing the influence of a weak and rapid noise from one dominating source, e.g. the kinetic equations describing a…

Even under constant external conditions, the expression levels of genes fluctuate. Much emphasis has been placed on the components of this noise that are due to randomness in transcription and translation; here we analyze the role of noise…

We show how the evolution of atoms in a tilted lattice can be changed and controlled by phase noise on the lattice. Dependent on the characteristic parameters of the noise, the interband transport can either be suppressed or enhanced, which…

The presence of noise in non linear dynamical systems can play a constructive role, increasing the degree of order and coherence or evoking improvements in the performance of the system. An example of this positive influence in a biological…

This work is devoted to investigating the evolution of concentration in a genetic regulation system, when the synthesis reaction rate is under additive and multiplicative asymmetric stable L\'evy fluctuations. By focusing on the impact of…

This paper is devoted to investigating the random dynamics of stochastic discrete long-wave-short-wave resonance equations, which are characterized by the following features: $(1)$ the equations contain locally Lipschitz nonlinear coupling…

We formulate the stochastic dynamics of a particle subject to internal non-white (coloured) noise in terms of path-integrals. In the simplest case, where the noise is exponentially correlated, the weak-noise limit is characterised by…