Related papers: Morphological stability and identity in self-organ…
We present a simple discrete model for the non-linear spatial interaction of different kinds of ``subpopulations'' composed of identical moving entities like particles, bacteria, individuals, etc. The model allows to mimic a variety of…
Motivated by the idea of using simple macroscopic examples to illustrate the physics of complex systems, we modify a historic experimental setup in which interacting floating magnets spontaneously self-assemble into ordered clusters. By…
We study discrete dynamical systems through the topological concepts of limit set, which consists of all points that can be reached arbitrarily late, and asymptotic set, which consists of all adhering values of orbits. In particular, we…
We describe a mathematical formalism and numerical algorithms for identifying and tracking slowly mixing objects in nonautonomous dynamical systems. In the autonomous setting, such objects are variously known as almost-invariant sets,…
A novel model of biological organisms is advanced, treating an organism as a self-consistent system subject to a pathogen flux. The principal novelty of the model is that it describes not some parts, but a biological organism as a whole.…
The study of the interplay between the structure and dynamics of complex multilevel systems is a pressing challenge nowadays. In this paper, we use a semi-annealed approximation to study the stability properties of Random Boolean Networks…
In this study, we performed comprehensive morphological investigations of the spontaneous formations of effective network structures among elements in coupled logistic maps, specifically with a delayed connection change. Our proposed model…
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…
To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develop various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develop…
A well-known property of unordered configuration spaces of points (in an open, connected manifold) is that their homology stabilises as the number of points increases. We generalise this result to moduli spaces of submanifolds of higher…
A simple relation of the order of $n$ abstract objects generates an $n-2$ dimensional basis of three dimensional vectors. A cellular automaton-like model of evolution of this system is postulated. During this evolution, some quantities…
Our technologies complexify our environments. Thus, new technologies need to deal with more and more complexity. Several efforts have been made to deal with this complexity using the concept of self-organization. However, in order to…
Interacting, self-propelled particles such as epithelial cells can dynamically self-organize into complex multicellular patterns, which are challenging to classify without a priori information. Classically, different phases and phase…
Soil is a complex, dynamic material, with physical properties that depend on its biological content. We propose a cellular automaton model for self-organizing soil structure, where soil aggregates and serves as food for microbial species.…
Species or population that proliferate faster than others become dominant in numbers. Catalysis allows catalytic sets within a molecular reaction network to dominate the non catalytic parts of the network by processing most of the available…
This paper aims at providing a rigorous definition of self- organization, one of the most desired properties for dynamic systems (e.g., peer-to-peer systems, sensor networks, cooperative robotics, or ad-hoc networks). We characterize…
What determines biodiversity in nature is a prominent issue in ecology, especially in biotic resource systems that are typically devoid of cross-feeding. Here, we show that by incorporating pairwise encounters among consumer individuals…
We show how singularities shape the evolution of rational discrete dynamical systems. The stabilisation of the form of the iterates suggests a description providing among other things generalised Hirota form, exact evaluation of the…
Deterministic many-body systems governed by simple interactions can self-organize into macroscopic patterns, and the determinants of long-time behavior are assumed to be encoded in the initial configuration. Here we show that predictability…
We introduce structural heterogeneity, a new topological characteristic for semi-ordered materials that captures their degree of organisation at a mesoscopic level and tracks their time-evolution, ultimately detecting the order-disorder…