We consider Constrained Semi-Assignment Problems, where one has to optimally assign discrete values to decision variables, and where furthermore logical constraints restrict the set of feasible assignments. We present a heuristic approach based on a continuous relaxation. More precisely, we consider a discrete dynamical system evolving in the interior of a polytope whose extremal points corresp...

Some characterizations on the chain recurrence, chain transitivity, chain mixing property,shadowing and $h$-shadowing for Zadeh's extension are obtained. Besides, it is provedthat a dynamical system is spatiotemporally chaotic provided that the Zadeh's extensionis Li-Yorke sensitive.

The aim of this paper is to introduce a method for computing rigorous lower bounds for topological entropy. The topological entropy of a dynamical system measures the number of trajectories that separate in finite time and quantifies the complexity of the system. Our method relies on extending existing computational Conley index techniques for constructing semi-conjugate symbolic dynamical syst...

We develop an Onsager-Machlup-type theory for nonequilibrium semi-Markov processes. Our main result is an exact large time asymptotics for the joint probability of the occupation times and the currents in the system, establishing some generic large deviation structures. We discuss in detail how the nonequilibrium driving and the non-exponential waiting time distribution influence the occupation...

In this paper, global uniform exponential stability of perturbed dynamical systems is studied by using Lyapunov techniques. The system presents a perturbation term which is bounded by an integrable function with the assumption that the nominal system is globally uniformly exponentially stable. Some examples in dimensional two are given to illustrate the applicability of the main results.

Given a heuristic estimate of the relative safety of a hybrid dynamical system trajectory, we transform the initial safety problem for dynamical systems into a global optimization problem. We introduce MLLO-IQ and MLLO-RIQ, two new information-based optimization algorithms. After demonstrating their strengths and weaknesses, we describe the class of problems for which diierent optimization meth...

We provide a rather general perfection result for crude local semi-flows taking values in Polish space showing that semi-flow has modification which is (perfect) invariant under suitable metric dynamical system. Such (local) induces random system (RDS). Then we show this can be applied to several classes of stochastic differential equations driven by semimartingales with stationary increments s...

Given a heuristic estimate of the relative safety of a hybrid dynamical system trajectory, we transform the initial safety problem for dynamical systems into a global optimization problem. We compare untuned performance of several Simulated Annealing and Multi Level Single Linkage method variants, and discuss the dynamic use of knowledge gained during optimization.

Given a heuristic estimate of the relative safety of a hybrid dynamical system trajectory, we transform the initial safety problem for dynamical systems into a global optimization problem. We compare un-tuned performance of several Simulated Annealing and Multi Level Single Linkage method variants, and discuss the dynamic use of knowledge gained during optimization.

In this paper, we introduce a new hyperchaotic complex T-system. This system has complex nonlinear behavior which we study its dynamical properties including invariance, equilibria and their stability, Lyapunov exponents, bifurcation, chaotic behavior and chaotic attractors as well as necessary conditions for this system to generate chaos. We discuss the synchronization with certain and uncerta...