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We consider the dynamics of a population of organisms containing two mutually inhibitory gene regulatory networks, that can result in a bistable switch-like behaviour. We completely characterize their local and global dynamics in the…
Driven suspensions, where energy is input at a particle scale, are a framework for understanding general principles of out-of-equilibrium organization. A large number of simple interacting units can give rise to non-trivial structure and…
Nucleation of domain walls by current-driving a single domain wall, confined to the junction area of two symmetrical strips, is investigated using systematic micromagnetic simulations. Secondary domain walls (equivalently, bits encoded in…
Due to the vast design space of molecules, generating molecules conditioned on a specific sub-structure relevant to a particular function or therapeutic target is a crucial task in computer-aided drug design. Existing works mainly focus on…
Coupling diffusion process of signaling molecules with nonlinear interactions of intracellular processes and cellular growth/transformation leads to a system of reaction-diffusion equations coupled with ordinary differential equations…
In experiments on model membranes, a formation of large domains of different lipid composition is readily observed. However, no such phase separation is observed in the membranes of intact cells. Instead, a structure of small transient…
Using agent-based simulations of self-propelled particles subject to short-range repulsion and nematic alignment we explore the dynamical phases of a dense active material confined to the surface of a sphere. We map the dynamical phase…
Simulations show that when a phase-separated binary AB fluid is driven to flow past chemically patterned substrates in a microchannel, the fluid exhibits unique morphological instabilities. For the pattern studied, these instabilities give…
In this work, we investigate a model of an adaptive networked dynamical system, where the coupling strengths among phase oscillators coevolve with the phase states. It is shown that in this model the oscillators can spontaneously…
Reaction-diffusion models have been used over decades to study biological systems. In this context, evolution equations for probability distribution functions and the associated stochastic differential equations have nowadays become…
We explore pattern formation in an active fluid system involving two chemical species that regulate active stress: a fast-diffusing species ($A$) and a slow-diffusing species ($I$). The growth of species $A$ is modelled using a nonlinear…
The membrane components of cellular organelles have been shown to segregate into domains as the result of biochemical maturation. We propose that the dynamical competition between maturation and lateral segregation of membrane components…
Active agents with time-delayed interactions arise naturally in various real-world systems, such as biological systems, transportation networks and robotic swarms. Such systems are typically modeled as Delay Differential Equations (DDEs)…
In this work we show that under specific anomalous diffusion conditions, chemical systems can produce well-ordered self-similar concentration patterns through a diffusion-driven instability. We also find spiral patterns and patterns with…
Diffusion processes are instrumental to describe the movement of a continuous quantity in a generic network of interacting agents. Here, we present a probabilistic framework for diffusion in networks and propose to classify agent…
Spontaneous pattern formation in a variety of spatially extended nonlinear system always occurs through a modulation instability: homogeneous state of the system becomes unstable with respect to growing modulation modes. Therefore, the…
The study of pattern emergence together with exploration of the exemplar Turing model is enjoying a renaissance both from theoretical and experimental perspective. Here, we implement a stability analysis of spatially dependent reaction…
We describe various types of traveling fronts of bistable reaction-diffusion cellular automata. These dynamical systems with discrete time, space, and state spaces can be seen as fully discrete versions of widely studied bistable…
Biomolecular condensates help organize the cell cytoplasm and nucleoplasm into spatial compartments with different chemical compositions. A key feature of such compositional patterning is the local enrichment of enzymatically active…
A model for single-domain uniaxial ferromagnetic particles with high anisotropy, the Ising model, is studied. Recent experimental observations have been made of the probability that the magnetization has not switched. Here an approach is…