Related papers: Semipredictable dynamical systems
We say that a finite asynchronous cellular automaton (or more generally, any sequential dynamical system) is pi-independent if its set of periodic points are independent of the order that the local functions are applied. In this case, the…
We show that a wide variety of non-linear cellular automata (CAs) can be decomposed into a quasidirect product of linear ones. These CAs can be predicted by parallel circuits of depth O(log^2 t) using gates with binary inputs, or O(log t)…
A transition from asymmetric to symmetric patterns in time-dependent extended systems is described. It is found that one dimensional cellular automata, started from fully random initial conditions, can be forced to evolve into complex…
Topological dynamics of cellular automata (CA), inherited from classical dynamical systems theory, has been essentially studied in dimension 1. This paper focuses on higher dimensional CA and aims at showing that the situation is different…
Linear dynamical systems are canonical models for learning-based control of plants with uncertain dynamics. The setting consists of a stochastic differential equation that captures the state evolution of the plant understudy, while the true…
This paper introduces Differentiable Logic Cellular Automata (DiffLogic CA), a novel combination of Neural Cellular Automata (NCA) and Differentiable Logic Gates Networks (DLGNs). The fundamental computation units of the model are…
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…
This paper proposes an algorithm capable of driving a system to follow a piecewise linear trajectory without prior knowledge of the system dynamics. Motivated by a critical failure scenario in which a system can experience an abrupt change…
This paper introduces a simple formalism for dealing with deterministic, non- deterministic and stochastic cellular automata in an unified and composable manner. This formalism allows for local probabilistic correlations, a feature which is…
The phase diagram of the coupled sine circle map lattice shows spatio-temporal intermittency of two distinct types: spatio-temporal intermittency of the directed percolation (DP) class, and spatial intermittency which does not belong to…
We demonstrate that a local mapping f in a space of bisequences over {0,1} which conserves the number of nonzero sites can be viewed as a deterministic particle system evolving according to a local mapping in a space of increasing…
Cellular automata are both computational and dynamical systems. We give a complete classification of the dynamic behaviour of elementary cellular automata (ECA) in terms of fundamental dynamic system notions such as sensitivity and…
This study aims at finding a method for constructing molecular dynamics like models using the formalism of cellular automata for fast simulation of fluid dynamic systems (including compressible phenomena). In as much as the results…
We consider dynamical semigroups with unbounded Kossakowski-Lindblad-Davies generators which are related to evolution of an open system with a tuned repeated harmonic perturbation. Our main result is the proof of existence of uniquely…
Chaos is omnipresent in nature, and its understanding provides enormous social and economic benefits. However, the unpredictability of chaotic systems is a textbook concept due to their sensitivity to initial conditions, aperiodic behavior,…
We propose a four-way classification of two-dimensional semi-totalistic cellular automata that is different than Wolfram's, based on two questions with yes-or-no answers: do there exist patterns that eventually escape any finite bounding…
In this paper, we study the probabilistic stability analysis of a subclass of stochastic hybrid systems, called the Planar Probabilistic Piecewise Constant Derivative Systems (Planar PPCD), where the continuous dynamics is deterministic,…
Wolfram has provided a qualitative classification of cellular automata(CA) rules according to which, there exits a class of CA rules (called Class 4) which exhibit complex pattern formation and long-lived dynamical activity (long…
The probabilistic cellular automaton (PCA) method is highlighted for its relatively simple numerical algorithm and low computational cost in the simulation of microstructural evolution. In this method, probabilistic state change rules are…
In this paper we study the space evolution in the Rule 54 reversible cellular automaton, which is a paradigmatic example of a deterministic interacting lattice gas. We show that the spatial translation of time configurations of the…