Related papers: Spatial organization and evolutional period of the…
Alexander B. Medvinsky \emph{et al} [A. B. Medvinsky, I. A. Tikhonova, R. R. Aliev, B.-L. Li, Z.-S. Lin, and H. Malchow, Phys. Rev. E \textbf{64}, 021915 (2001)] and Marcus R. Garvie \emph{et al} [M. R. Garvie and C. Trenchea, SIAM J.…
Excitable media are a generic class of models used to simulate a wide variety of natural systems including cardiac tissue. Propagation of excitation waves in this medium results in the formation of characteristic patterns such as rotating…
We show that autocatalytic networks of epsilon-machines and their population dynamics differ substantially between spatial (geographically distributed) and nonspatial (panmixia) populations. Generally, regions of spacetime-invariant…
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…
We study the dynamics of (synchronous) one-dimensional cellular automata with cyclical boundary conditions that evolve according to the majority rule with radius $ r $. We introduce a notion that we term cell stability with which we express…
A diffusive epidemic model with an infection-dependent recovery rate is formulated in this paper. Multiple constant steady states and spatially homogeneous periodic solutions are first proven by bifurcation analysis of the reaction…
We report experimental evidence of the route to spatiotemporal chaos in a large 1D-array of hotspots in a thermoconvective system. Increasing the driving force, a stationary cellular pattern becomes unstable towards a mixed pattern of…
Contemporary epidemiological models often involve spatial variation, providing an avenue to investigate the averaged dynamics of individual movements. In this work, we extend a recent model by Vaziry, Kolokolnikov, and Kevrekidis [Royal…
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…
In this paper, we present stochastic synchronous cellular automaton defined on a square lattice. The automaton rules are based on the SEIR (susceptible $\to$ exposed $\to$ infected $\to$ recovered) model with probabilistic parameters…
We identify a new type of pattern formation in spatially distributed active systems. We simulate one-dimensional two-component systems with predator-prey local interaction and pursuit-evasion taxis between the components. In a sufficiently…
We investigate a model for spatial epidemics explicitly taking into account bi-directional movements between base and destination locations on individual mobility networks. We provide a systematic analysis of generic dynamical features of…
We investigate the Susceptible-Infectious-Recovered contagion dynamics in a system of self-propelled particles with polar alignment. Using agent-based simulations, we analyze the outbreak process for different combinations of the spatial…
We consider the SEIRS epidemiology model with such features of the COVID-19 outbreak as: abundance of unidentified infected individuals, limited time of immunity and a possibility of vaccination. The control of the pandemic dynamics is…
We show techniques of analyzing complex dynamics of cellular automata (CA) with chaotic behaviour. CA are well known computational substrates for studying emergent collective behaviour, complexity, randomness and interaction between order…
Nonlinear reaction-diffusion systems admit a wide variety of spatiotemporal patterns or structures. In this lecture, we point out that there is certain advantage in studying discrete arrays, namely cellular neural/nonlinear networks (CNNs),…
The spread of viruses in biological networks, computer networks, and human contact networks can have devastating effects; developing and analyzing mathematical models of these systems can be insightful and lead to societal benefits. Prior…
We study the time evolution of perturbations in spatially extended chaotic systems in the presence of quenched disorder. We find that initially random perturbations tend to exponentially localize in space around static pinning centers that…
The spatiotemporal structure of reactive media supporting a solitary spiral wave is studied for systems where the local reaction law exhibits a period-doubling cascade to chaos. This structure is considerably more complex than that of…
We consider discrete-time random perturbations of monotone cellular automata (CA) in two dimensions. Under general conditions, we prove the existence of half-space velocities, and then establish the validity of the Wulff construction for…