There is a growing recognition of the presence of dynamical systems in many fields. In areas ranging from economics to physics and computer science to biology, many open fundamental problems are known to relate to the central problems in dynamical systems theory. Physicists generally work more with continuous dynamical systems, rather than discrete dynamical systems which computer scientists ma...

A dynamical system is by definition a system whose state changes with time t. We have a discrete dynamical system when t is an integer or a natural number, and the elements of the system can be obtained in the form u t+1 = F(u t ), where F is some global function which describes the evolution rule of the system (see [1]). In a series of very recentworks, the theory of discrete dynamical systems...

While the notion of chaos is well established for dynamical systems on manifolds, it is not so for dynamical systems over discrete spaces with N variables, as binary neural networks and cellular automata. The main difficulty is the choice of a suitable topology to study the limit N → ∞. By embedding the discrete phase space into a Cantor set we provided a natural setting to define topological e...

In this paper we address the question of the expressibility of discrete event speciied systems (DEVS), i.e., we characterize the subclass of dynamical systems which can be homomorphically represented by DEVS models. We show that causal dynamical systems with piecewise constant input and output segment spaces are DEVS-representable. Moreover, DEVS-representable dynamical systems are closed under...

in this paper we proposed a cellular automaton based local algorithm to solve the autonomously sensor gathering problem in mobile wireless sensor networks (mwsn). in this problem initially the connected mobile sensors deployed in the network and goal is gather all sensors into one location. the sensors decide to move only based on their local information. cellular automaton (ca) as dynamical sy...

‎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...

In this paper, we discuss delayed periodic dynamical systems, compare capability of criteria of global exponential stability in terms of various L (1 ≤ p < ∞) norms. A general approach to investigate global exponential stability in terms of various L (1 ≤ p < ∞) norms is given. Sufficient conditions ensuring global exponential stability are given, too. Comparisons of various stability criteria ...

The purpose of this article is to serve as a light-weight introduction into the mysteries of analog and hybrid computing models from a dynamical systems and programming languages perspective. Hybrid systems are the dynamical systems that combine both models of computation, i.e., have interacting discrete and continuous dynamics. They have found widespread application as models for embedded comp...