‎In this text we prove that in generalized shift dynamical system $(X^Gamma,sigma_varphi)$‎ ‎for finite discrete $X$ with at least two elements‎, ‎infinite countable set $Gamma$ and‎ ‎arbitrary map $varphi:GammatoGamma$‎, ‎the following statements are equivalent‎: ‎ - the dynamical system $(X^Gamma,sigma_varphi)$ is‎ Li-Yorke chaotic;‎ - the dynamical system $(X^Gamma,sigma_varphi)$ has‎ an scr...

We establish a relationship between general constrained pseudoconvex optimization problems and globally projected dynamical systems. A corresponding novel neural network model, which is globally convergent and stable in the sense of Lyapunov, is proposed. Both theoretical and numerical approaches are considered. Numerical simulations for three constrained nonlinear optimization problems a...

In this paper, we present a dynamical systems approach to material damage identification. This methodology does not depend on knowledge of the particular damage physics of material fatigue. Instead, it provides experimental means to determine what are practically observable and observed facts of damage accumulation, thus making it possible to develop or experimentally verify appropriate damage ...

In this paper, we introduce a notion of property (T) for a C<span style="font-family: txsy; font-size: 7pt; color: #000000; font-style: norm...

In this note some useful properties of strongly continuous two-parameter semigroups of operators are studied, an exponential formula for two-parameter semigroups of operators on Banach spaces is obtained and some applied examples of two-parameter dynamical systems are discussed

This paper addresses the parameter estimation problem of an interval-based hybrid dynamical system (interval system). The interval system has a two-layer architecture that comprises a finite state automaton and multiple linear dynamical systems. The automaton controls the activation timing of the dynamical systems based on a stochastic transition model between intervals. Thus, the interval syst...

In this paper we introduce the concept of entropy operator for continuous systems of finite topological entropy. It is shown that it generates the Kolmogorov entropy as a special case. If $phi$ is invertible then the entropy operator is bounded with the topological entropy of $phi$ as its norm.