Related papers: Spatio-temporal Pattern Formation due to Host-Circ…

Motivated by bacterial chemotaxis and multi-species ecological interactions in heterogeneous environments, we study a general one-dimensional reaction-cross-diffusion system in the presence of spatial heterogeneity in both transport and…

We report experimental and theoretical results on spatiotemporal pattern formation in cell populations, where the parameters vary in space and time due to mechanisms intrinsic to the system, namely Dictyostelium discoideum (D.d.) in the…

In the present work, we explore the influence of habitat complexity on the activities of prey and predator of a spatio-temporal system by incorporating self diffusion. First we modify the Rosenzweig-MacArthur predator-prey model by…

Spatio-temporal pattern formation over the square and rectangular domain has received significant attention from researchers. A wide range of stationary and non-stationary patterns produced by two interacting populations is abundant in the…

Many existing studies on pattern formation in the reaction-diffusion systems rely on deterministic models. However, environmental noise is often a major factor which leads to significant changes in the spatiotemporal dynamics. In this…

A local agglomeration of cooperators can support the survival or spreading of cooperation, even when cooperation is predicted to die out according to the replicator equation, which is often used in evolutionary game theory to study the…

We examine a spatially discrete reaction diffusion model based on the interactions that create a periodic pattern in the Drosophila eye imaginal disc. This model is capable of generating a regular hexagonal pattern of gene expression behind…

Pattern formation often occurs in confined systems, yet how boundaries shape patterning dynamics is unclear. We develop techniques to analyze confinement effects in nonlocal advection-diffusion equations, which generically capture the…

Reaction-diffusion systems have been widely used to study spatio-temporal phenomena in cell biology, such as cell polarization. Coupled bulk-surface models naturally include compartmentalization of cytosolic and membrane-bound polarity…

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…

Bacteria possess diverse mechanisms to regulate their motility in response to environmental and physiological signals, enabling them to navigate complex habitats and adapt their behavior. Among these mechanisms, interspecies recognition…

Bistability is a major mechanism for cellular decision making and usually results from positive feedback in biochemical control systems. Here we show theoretically that bistability between unbound and bound states of adhesion clusters…

In this paper, we study an excitable, biophysical system that supports wave propagation of nerve impulses. We consider a slow-fast, FitzHugh-Rinzel neuron model where only the membrane voltage interacts diffusively, giving rise to the…

The spontaneous generation of electrical activity underpins a number of essential physiological processes, and is observed even in tissues where specialized pacemaker cells have not been identified. The emergence of periodic oscillations in…

This paper addresses the question of how population diffusion affects the formation of the spatial patterns in the spatial epidemic model by Turing mechanisms. In particular, we present theoretical analysis to results of the numerical…

Collective behavior of bacterial colonies plays critical roles in adaptability, survivability, biofilm expansion and infection. We employ an individual-based model of an interstitial biofilm to study emergent pattern formation based on the…

In this paper, we investigate the emergence of a predator-prey model with Beddington-DeAngelis-type functional response and reaction-diffusion. We derive the conditions for Hopf and Turing bifurcation on the spatial domain. Based on the…

The processes in nonequilibrium dissipative media caused by coherent structure formation and lead to the complicated dynamics are of interest for nonlinear physics. Here we consider a model of the flow of interacting electronics patterns.…

We derive an equation that governs the spatiotemporal dynamics of small amplitude alternans in paced cardiac tissue. We show that a pattern-forming linear instability leads to the spontaneous formation of stationary or traveling waves whose…

The costly provision of public goods serves as a model problem for the evolution of cooperative behavior, presenting a social dilemma between the collective benefits of shared resources and the individual incentive to free-ride in resource…