Related papers: Semipredictable dynamical systems
We present a new type of deterministic dynamical behaviour that is less predictable than white noise. We call it anti-deterministic (AD) because time series corresponding to the dynamics of such systems do not generate deterministic lines…
Complex systems are commonly modeled using nonlinear dynamical systems. These models are often high-dimensional and chaotic. An important goal in studying physical systems through the lens of mathematical models is to determine when the…
Chaotic systems are intrinsically sensitive to small errors, challenging efforts to construct predictive data-driven models of real-world dynamical systems such as fluid flows or neuronal activity. Prior efforts comprise either specialized…
Number-conserving (or {\em conservative}) cellular automata have been used in several contexts, in particular traffic models, where it is natural to think about them as systems of interacting particles. In this article we consider several…
We present an approach to construct approximate Koopman-type decompositions for dynamical systems depending on static or time-varying parameters. Our method simultaneously constructs an invariant subspace and a parametric family of…
The Cellular Automaton (CA) modeling and simulation of solid dynamics is a long-standing difficult problem. In this paper we present a new two-dimensional CA model for solid dynamics. In this model the solid body is represented by a set of…
We demonstrate that the concept of a conservation law can be naturally extended from deterministic to probabilistic cellular automata (PCA) rules. The local function for conservative PCA must satisfy conditions analogous to conservation…
Real-world computers have operational constraints that cause nonzero entropy production (EP). In particular, almost all real-world computers are ``periodic'', iteratively undergoing the same physical process; and ``local", in that…
We consider the problem of learning a non-deterministic probabilistic system consistent with a given finite set of positive and negative tree samples. Consistency is defined with respect to strong simulation conformance. We propose learning…
The problem of synthesizing stochastic explicit model predictive control policies is known to be quickly intractable even for systems of modest complexity when using classical control-theoretic methods. To address this challenge, we present…
In complex systems, groups of interacting objects may form prevalent and persistent spatiotemporal patterns, which we refer to as motifs. These motifs can exhibit features that reveal how individual objects interact with one another.…
Decomposition of state spaces into dynamically different components is helpful for the understanding of dynamical behaviors of complex systems. A Conley type decomposition theorem is proved for nonautonomous dynamical systems defined on a…
Cellular automata provide a fascinating class of dynamical systems capable of diverse complex behavior. These include simplified models for many phenomena seen in nature. Among other things, they provide insight into self-organized…
We study the computational complexity theory of smooth, finite-dimensional dynamical systems. Building off of previous work, we give definitions for what it means for a smooth dynamical system to simulate a Turing machine. We then show that…
Layered Cellular Automata (LCA) extends the concept of traditional cellular automata (CA) to model complex systems and phenomena. In LCA, each cell's next state is determined by the interaction of two layers of computation, allowing for…
The cellular automata discrete dynamical system is considered as the two-stage process: the majority rule for the change in the automata state and the rule for the change in topological relations between automata. The influence of changing…
One-dimensional quantum cellular automata (QCA) consist in a line of identical, finite dimensional quantum systems. These evolve in discrete time steps according to a local, shift-invariant unitary evolution. By local we mean that no…
Dynamical behaviour of discrete dynamical systems has been investigated extensively in the past few decades. However, in several applications, long term memory plays an important role in the evolution of dynamical variables. The definition…
This work builds on an existing model of discrete canonical evolution and applies it to the general case of a linear dynamical system, i.e., a finite-dimensional system with configuration space isomorphic to $ \mathbb{R}^{q} $ and linear…
We consider discrete and integer-valued cellular automata (CA). A particular class of which comprises "Hamiltonian CA" with equations of motion that bear similarities to Hamilton's equations, while they present discrete updating rules. The…