Related papers: Pattern formation by competition: a biological exa…
Boundary-induced pattern formation from a spatially uniform state is investigated using one-dimensional reaction-diffusion equations. The temporal oscillation is successively transformed into a spatially periodic pattern, triggered by…
This study investigates the role of spatial segregation, prompted by competition avoidance, as a key mechanism for emergent coexistence within microbial communities. Recognizing these communities as complex adaptive systems, we challenge…
Molecular dynamics simulations and integral equation calculations of a simple equimolar mixture of diatomic molecules and monomers interacting via attractive and repulsive short-range potentials show the existence of pattern formation…
We investigate noise-induced pattern formation in a model of cancer growth based on Michaelis-Menten kinetics, subject to additive and multiplicative noises. We analyse stability properties of the system and discuss the role of diffusion…
We consider here the morphogenesis (pattern formation) problem for some genetic network models. First, we show that any given spatio-temporal pattern can be generated by a genetic network involving a sufficiently large number of genes.…
This paper studies how patterns derived from a system of reaction-diffusion equations may vary significantly depending upon boundary and initial conditions, as well as in the spatial dependence of the coefficients involved. From an…
During bouts of evolutionary diversification, such as adaptive radiations, the emerging species cluster around different locations in phenotype space, How such multimodal patterns in phenotype space can emerge from a single ancestral…
We propose a technique to detect and generate patterns in a network of locally interacting dynamical systems. Central to our approach is a novel spatial superposition logic, whose semantics is defined over the quad-tree of a partitioned…
The periodic swarming of bacteria is one of the simplest examples for pattern formation produced by the self-organized collective behavior of a large number of organisms. In the spectacular colonies of Proteus mirabilis (the most common…
Reaction-diffusion systems may lead to the formation of steady state heterogeneous spatial patterns, known as Turing patterns. Their mathematical formulation is important for the study of pattern formation in general and play central roles…
In order to better understand the interplay of partnership and competition in population dynamics we study a family of generalized May-Leonard models with $N$ species. These models have a very rich structure, characterized by different…
Vegetation patterns are abundant in arid and semiarid ecosystems, but how they form remains unclear. One of the most extended theories lies in the existence of scale-dependent feedbacks (SDF) in plant-to-plant and plant-water interactions.…
Recent work suggests that cross-feeding -- the secretion and consumption of metabolic biproducts by microbes -- is essential for understanding microbial ecology. Yet how cross-feeding and competition combine to give rise to ecosystem-level…
We study the formation of spot patterns seen in a variety of bacterial species when the bacteria are subjected to oxidative stress due to hazardous byproducts of respiration. Our approach consists of coupling the cell density field to a…
Motile bacteria can migrate along chemical gradients in a process known as chemotaxis. When exposed to uniform environmental stress, Escherichia coli cells coordinate their chemotactic responses to form millimeter-sized condensates…
The bacterium {\em Bacilus subtilis} frequently forms biofilms at the interface between the culture medium and the air. We develop a mathematical model that couples a description of bacteria as individual discrete objects to the standard…
Biological and social systems are structured at multiple scales, and the incentives of individuals who interact in a group may diverge from the collective incentive of the group as a whole. Mechanisms to resolve this tension are responsible…
Reaction-diffusion systems have been proposed as a model for pattern formation and morphogenesis. The Fickian diffusion typically employed in these constructions model the Brownian motion of particles. The biological and chemical elements…
A model of pattern formation in living systems is presented. The pattern is achieved by the sequential interaction of two signaling pathways. The coupling of the pattern to the (thick) epithelial sheet changes is given, when the Gauss…
The solution space of genome-scale models of cellular metabolism provides a map between physically viable flux configurations and cellular metabolic phenotypes described, at the most basic level, by the corresponding growth rates. By…