The paper considers some concepts of nonuniform asymptotic stability for skew-evolution semiflows on Banach spaces. The obtained results clarify differences between the uniform and nonuniform cases. Some examples are included to illustrate the results.

We discuss the evolution of the fluctuations in a symmetric φ c-exponential potential which provides a power-law expansion during inflation using both, the gauge invariant field Φ and the Sasaki-Mukhanov field.

We explore the simulation and computational capabilities of dynamical systems We rst introduce and compare several notions of simulation between discrete systems We give a general framework that allows dynamical systems to be considered as computational machines We introduce a new discrete model of computation the analog automaton model We determine the computational power of this model and pro...

The controversial concept of quantum chaos – the dynamical chaos in bounded mesoscopic quantum systems – is presented as the most important and universal instance of a new generic dynamical phenomenon: pseudochaos. The latter characterizes the irregular behaviour of dynamical systems with discrete energy and/or frequency spectrum, which include classical systems with discrete phase space. The q...

We explore the simulation and computational capabilities of hybrid and continuous dynamical systems. The continuous dynamical systems considered are ordinary diierential equations (ODEs). For hybrid systems we concentrate on models that combine ODEs and discrete dynamics (e.g., nite automata). We review and compare four such models from the literature. Notions of simulation of a discrete dynami...

Hybrid systems have so far served us well throughout this course as a model for cyberphysical systems [Pla08, Pla10b]. Most definitely, hybrid systems can also serve as models for other systems that are not cyber-physical per se, i.e. they are not built as a combination of cyber and computing capabilities with physical capabilities. Some biological systems can be understood as hybrid systems, b...

This paper is concerned with stability analysis of biological networks modeled as discrete and finite dynamical systems. We show how to use algebraic methods based on quantifier elimination, real solution classification and discriminant varieties to detect steady states and to analyze their stability and bifurcations for discrete dynamical systems. For finite dynamical systems, methods based on...

This paper treats a nonlinear dynamical system with both continuous-time and discrete-time variables as a differential–difference–algebraic equation (DDA) or a hybrid dynamical system, presents a fundamental analyzing method of such a DDA system for local sampling, asymptotical stability, singular perturbations and bifurcations, and further shows that there exist four types of generic codimensi...

We study the logic of dynamical systems, that is, logics and proof principles for properties of dynamical systems. Dynamical systems are mathematical models describing how the state of a system evolves over time. They are important for modeling and understanding many applications, including embedded systems and cyber-physical systems. In discrete dynamical systems, the state evolves in discrete...