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Distribution-dependent stochastic dynamical systems arise widely in engineering and science. We consider a class of such systems which model the limit behaviors of interacting particles moving in a vector field with random fluctuations. We…
We investigate a stochastic search process in one dimension under the competing roles of mortality, redundancy, and diversity of the searchers. This picture represents a toy model for the fertilization of an oocyte by sperm. A population of…
The study of biological cells in terms of mesoscopic, nonequilibrium, nonlinear, stochastic dynamics of open chemical systems provides a paradigm for other complex, self-organizing systems with ultra-fast stochastic fluctuations, short-time…
Cell migration is a fundamental process involved in physiological phenomena such as the immune response and morphogenesis, but also in pathological processes, such as the development of tumor metastasis. These functions are effectively…
One-dimensional hopping model is useful to describe the motion of microscopic particle in thermal noise environment, such as motor proteins. Recent experiments about the new generation of light-driven rotary molecular motors found that, the…
Experiments, in particular on biological systems, typically probe lower-dimensional observables which are projections of high-dimensional dynamics. In order to infer consistent models capturing the relevant dynamics of the system, it is…
We consider the problem of selecting deterministic or stochastic models for a biological, ecological, or environmental dynamical process. In most cases, one prefers either deterministic or stochastic models as candidate models based on…
In the last decade, stochastic models have shown to be very useful for quantitative modelling of social processes. Here, a configurational master equation for the description of behavioral changes by pair interactions of individuals is…
Spontaneous structural rearrangements play a central role in the organization and function of complex biomolecular systems. In principle, physics-based computer simulations like Molecular Dynamics (MD) enable us to investigate these…
Stochastic Differential Equations (SDEs) serve as a powerful modeling tool in various scientific domains, including systems science, engineering, and ecological science. While the specific form of SDEs is typically known for a given…
The canonical model of stochastic search tracks a randomly diffusing "searcher" until it finds a "target." Owing to its many applications across science and engineering, this perennially popular problem has been thoroughly investigated in a…
Complex systems often have features that can be modeled by advanced mathematical tools [1]. Of special interests are the features of complex systems that have a network structure as such systems are important for modeling technological and…
This paper introduces a linear state-space model with time-varying dynamics. The time dependency is obtained by forming the state dynamics matrix as a time-varying linear combination of a set of matrices. The time dependency of the weights…
We consider the driven dynamics of a probe particle moving through an assembly of particles with competing long-range repulsive and short-range attractive interactions, which form crystal, stripe, labyrinth, and bubble states as the ratio…
Stochastic dynamics of chemical reactions in a mutually repressing two-gene circuit is numerically simulated. The circuit has a rich variety of different states when the kinetic change of DNA status is slow. The stochastic switching…
Switching interacting particle systems studied in probability theory are the stochastic processes of hopping particles on a lattice made up of slow and fast particles, where the switching between these types of particles occurs randomly at…
We give a very short introduction to discrete and continuum models for the evolutionary and spatial dynamics of cancer through two case studies: a model for the evolutionary dynamics of cancer cells under cytotoxic therapy and a model for…
Density-dependent diffusion is a widespread phenomenon in nature. We have examined the density-dependent diffusion behavior of some biological processes such as tumor growth and invasion [23]. Here, we extend our previous work by developing…
We analyze ecological systems that are influenced by random environmental fluctuations. We first provide general conditions which ensure that the species coexist and the system converges to a unique invariant probability measure (stationary…
Deterministic continuum models formulated in terms of non-local partial differential equations for the evolutionary dynamics of populations structured by phenotypic traits have been used recently to address open questions concerning the…