This paper shows how to compute, for probabilistic hybrid systems, the clock approximation and linear phase-portrait approximation that have been proposed for non probabilistic processes by Henzinger et al. The techniques permit to define a rectangular probabilistic process from a non rectangular one, hence allowing the model-checking of any class of systems. Clock approximation, which applies ...

We present splitting methods for numerically solving a certain class of explicitly time-dependent linear differential equations. Starting from an efficient method for the autonomous case and making use of the formal solution obtained with the Magnus expansion, we show how to get the order conditions for the non-autonomous case. We also build a family of sixth-order integrators whose performance...

We describe powerful computational techniques, relying on linear algebraic methods,for generating ideals of non-linear invariants of algebraic hybrid systems. We show thatthe preconditions for discrete transitions and the Lie-derivatives for continuous evolu-tion can be viewed as morphisms, and so can be suitably represented by matrices. Wereduce the non-trivial invariant genera...

Quantum dynamics of integrable systems is discussed. Localized wave packets generalizing the conventional coherent states of minimal uncertainty are constructed. The wave packet moves along a certain trajectory and does not change its shape for times of order 1 h̄ . In this Letter we suggest that the definition of a coherent state should be related to the Hamiltonian.The conventional coherent st...

This paper suggests a procedure for estimating excursion probabilities for linear and non-linear systems subjected to Gaussian excitation processes. In this paper, the focus is on non-linear systems which might also have stochastic properties. The approach is based on the so called “averaged excursion probability flow” which allows for a simple solution for the interaction in excursion problems...

We discuss the origins and recent advances of the vast field of non-linear dynamics and complex systems. The main aspects of complex systems are illustrated with relevant examples and the connection with non-linear dynamics and chaos is presented. Since this is a truly interdisciplinary field of research, many applications in mathematics, physics, chemistry, biology and physiology are briefly c...

This study investigates the impact of innovation on users of an evolving Information Systems (IS) product. Building on two different streams of research, Levitts (1980) Total Product Concept and the Three Factor theory (Kano. 1984) this study identifies three types of innovation: Basic, Expected and Augmented. The impact of introducing these innovations on user satisfaction was found to be depe...

AbstractThe paper involves thorough study of non-linear vibratory oscillators and numerical methodology to analyse and resolute the non-linear dynamical world. The study involves the analysis of non-linear oscillators like the Van der Pol Oscillator and Duffing Oscillator. Application of regular perturbation method in the oscillator is also demonstrated. The equilibrium and stability analysis o...

We present a framework to integrate the presentation and manipulation of several techniques for the interactive visualization of dynamical systems. The framework is inspired by the CAD metaphor and the “probes” metaphor. We present some examples and finally address some problematic

In this paper, the authors study chaos synchronization of chaotic systems, which can exhibit a two scroll attractor for different parameter values via linear feedback control. First, chaos synchronization of three dimensional systems is studied and ‘generalized non-linear dynamical systems’ are analyzed. The considered synchronization criterion consists of identical drive and response systems c...