Related papers: Strong stochastic stability of cellular automata
For deterministic monotone cellular automata on the $d$-dimensional integer lattice, Toom has given necessary and sufficient conditions for the all-one fixed point to be stable against small random perturbations. The proof of sufficiency is…
We investigate instabilities in a stochastic mathematical model of cochlear dynamics. The cochlea is modeled as a spatio-temporal dynamical system made up of a spatially distributed array of coupled oscillators, together with the cochlear…
In this article, we have proposed an epidemic model by using probability cellular automata theory. The essential mathematical features are analyzed with the help of stability theory. We have given an alternative modelling approach for the…
Despite being a foundational concept of modern systems theory, there have been few studies on observability of non-linear stochastic systems under partial observations. In this paper, we introduce a definition of observability for…
We give necessary and/or sufficient conditions for stochastic stability of second-order linear autonomous systems with parameters, which are perturbed by a random process of the "white noise" type. The Ito's and Stratonovich's forms of…
For deterministic monotone cellular automata on the $d$-dimensional integer lattice, Toom (1980) has given necessary and sufficient conditions for the all-one fixed point to be stable against small random perturbations. We are interested in…
The ever increasing complexity of real-time control systems results in significant deviations in the timing of sensing and actuation, which may lead to degraded performance or even instability. In this paper we present a method to analyze…
Stochastic models such as Continuous-Time Markov Chains (CTMC) and Stochastic Hybrid Automata (SHA) are powerful formalisms to model and to reason about the dynamics of biological systems, due to their ability to capture the stochasticity…
This work deals with the stability analysis of nonlinear sampled-data systems under nonuniform sampling. It establishes novel relationships between the stability property of the exact discrete-time model for a given sequence of (aperiodic)…
We consider random perturbations of discrete-time dynamical systems. We give sufficient conditions for the stochastic stability of certain classes of maps, in a strong sense. This improves the main result in J. F. Alves, V. Araujo, Random…
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…
Algorithmic stability is a central concept in statistics and learning theory that measures how sensitive an algorithm's output is to small changes in the training data. Stability plays a crucial role in understanding generalization,…
Neural cellular automata (NCA) provide a lightweight alternative to encoder-decoder segmentation networks. However, it can be difficult to decide when a prediction should be trusted. Here, we study uncertainty estimation for NCA-based…
This paper studies deterministic and stochastic fixed-time stability of autonomous nonlinear discrete-time (DT) systems. Lyapunov conditions are first presented under which the fixed-time stability of deterministic DT system is certified.…
In this paper, we investigate asymptotic stability of linear time-varying systems with (sub-) stochastic system matrices. Motivated by distributed dynamic fusion over networks of mobile agents, we impose some mild regularity conditions on…
Many different definitions of computational universality for various types of dynamical systems have flourished since Turing's work. We propose a general definition of universality that applies to arbitrary discrete time symbolic dynamical…
This paper addresses stochastic stabilization in case where implementation of control policies is digital, i. e., when the dynamical system is treated continuous, whereas the control actions are held constant in predefined time steps. In…
Randomly-assembled dynamical systems are theoretically predicted to be unstable upon crossing a critical threshold of complexity, as first shown by May. Yet, empirical complex systems exhibit remarkable stability, indicating the presence of…
In finite-dimensional dynamical systems, stochastic stability provides the selection of physical relevant measures from the myriad invariant measures of conservative systems. That this might also apply to infinite-dimensional systems is the…
Constraint tightening to non-conservatively guarantee recursive feasibility and stability in Stochastic Model Predictive Control is addressed. Stability and feasibility requirements are considered separately, highlighting the difference…