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Young's cellular automaton, recently applied to study the spatiotemporal evolution of binary patterns for favorable/hostile environments, has now been modified from a different point of view. In this model, each differentiated cell (DC)…
Traditional top-down robotic design often lacks the adaptability needed to handle real-world complexities, prompting the need for more flexible approaches. Therefore, this study introduces a novel cellular plasticity model tailored for…
How patterns and structures undergo symmetry breaking and self-organize within biological systems from initially homogeneous states is a key issue for biological development. The activator-inhibitor (AI) mechanism, derived from…
We rigorously prove a form of disorder-resistance for a class of one-dimensional cellular automaton rules, including some that arise as boundary dynamics of two-dimensional solidification rules. Specifically, when started from a random…
We study the pattern dynamics in a reaction diffusion model of the activator--inhibitor type in the oscillatory regime. We consider finite systems with partially absorptive boundary conditions analizing examples in different geometries in…
Understanding cell fate selection remains a central challenge in developmental biology. We present a class of simple yet biologically-motivated mathematical models for cell differentiation that generically generate oscillations and hence…
In the article a transition from pattern evolution equation of reaction-diffusion type to a cellular automaton (CA) is described. The applicability of CA is demonstrated by generating patterns of complex irregular structure on a hexagonal…
The Turing patterning mechanism is believed to underly the formation of repetitive structures in development, such as zebrafish stripes and mammalian digits, but it has proved difficult to isolate the specific biochemical species…
Pattern formation in biological tissues plays an important role in the development of living organisms. Since the classical work of Alan Turing, a pre-eminent way of modelling has been through reaction-diffusion mechanisms. More recently,…
Individual cellular automata rules are attractive models for a range of biological and physical self-assembling systems. While coexpression and coevolution are common in such systems, ensembles of cellular automata rules remain poorly…
Spatiotemporal patterns are common in biological systems. For electrically-coupled cells previous studies of pattern formation have mainly used external forcing as the main bifurcation parameter. The purpose of this paper is to show that…
Since its introduction in 1952, Turing's (pre-)pattern theory ("the chemical basis of morphogenesis") has been widely applied to a number of areas in developmental biology. The related pattern formation models normally comprise a system of…
We study reaction-diffusion systems beyond the Markovian approximation to take into account the effect of memory on the formation of spatio-temporal patterns. Using a non-Markovian Brusselator model as a paradigmatic example, we show how to…
We introduce simple models of genetic regulatory networks and we proceed to the mathematical analysis of their dynamics. The models are discrete time dynamical systems generated by piecewise affine contracting mappings whose variables…
Bacteria can form a great variety of spatially heterogeneous cell density patterns, ranging from simple concentric rings to dynamical spiral waves appearing in growing colonies. These pattern formation phenomena are important as they…
Inspired by active shape morphing in developing tissues and biomaterials, we investigate two generic mechanochemical models where the deformations of a thin elastic sheet are driven by, and in turn affect, the concentration gradients of a…
Although simulation models of geographical systems in general and agent-based models in particular represent a fantastic opportunity to explore socio-spatial behaviours and to test a variety of scenarios for public policy, the validity of…
The advances in understanding complex networks have generated increasing interest in dynamical processes occurring on them. Pattern formation in activator-inhibitor systems has been studied in networks, revealing differences from the…
Turing's mechanism is often invoked to explain periodic patterns in nature, although direct experimental support is scarce. Turing patterns form in reaction-diffusion systems when the activating species diffuse much slower than the…
In this paper we study the time evolution of a class of two-level systems driven by periodic fields in terms of new convergent perturbative expansions for the associated propagator U(t). The main virtue of these expansions is that they do…