Search results for "Systems Theory"

Numerical analysis of dynamical systems: unstable periodic orbits, hidden transient chaotic sets, hidden attractors, and finite-time Lyapunov dimensi…

2018

In this article, on the example of the known low-order dynamical models, namely Lorenz, Rossler and Vallis systems, the difficulties of reliable numerical analysis of chaotic dynamical systems are discussed. For the Lorenz system, the problems of existence of hidden chaotic attractors and hidden transient chaotic sets and their numerical investigation are considered. The problems of the numerical characterization of a chaotic attractor by calculating finite-time time Lyapunov exponents and finite-time Lyapunov dimension along one trajectory are demonstrated using the example of computing unstable periodic orbits in the Rossler system. Using the example of the Vallis system describing the El…

Stability analysis for stochastic hybrid systems: A survey

2014

This survey addresses stability analysis for stochastic hybrid systems (SHS), which are dynamical systems that combine continuous change and instantaneous change and that also include random effects. We re-emphasize the common features found in most of the models that have appeared in the literature, which include stochastic switched systems, Markov jump systems, impulsive stochastic systems, switching diffusions, stochastic impulsive systems driven by renewal processes, diffusions driven by Lévy processes, piecewise-deterministic Markov processes, general stochastic hybrid systems, and stochastic hybrid inclusions. Then we review many of the stability concepts that have been studied, inclu…

Chaotic Scattering in the Gaussian Potential

1995

It is well known that general classical Hamiltonian dynamical systems have as a rule chaotic behaviour. By such a term one usually understands a sensitive dependence on initial conditions which manifests itself in the topology of phase space. For the most studied case of bounded motions this behaviour is detected, for example, by analysing the Poincare surfaces of section and by calculating Lyapunov characteristic exponents. The question then naturally arises of what are the effects of this complexity on the unbounded motions, i.e., on scattering phenomena. The signature of chaotic dynamics in these scattering regions of phase space has been the object of several papers appeared mainly in t…

An Ecological Theory of Rational Interpretation

2005

The Joining of LiNbO3, Quartz, TlBr-TlI and Other Optical Materials by the Use of Thin Metal Films as Bonding Agents

2000

A method of joining ferroelectric, optical and other non-metallic materials, such as lithium niobate, quartz, TlBr-TlI, glass, etc., at room temperature under a pressure of 0.1÷0.5 MPa is described. The surfaces to be joined are prepared to optical flatness, and indium or lead coatings as bonding agents are used. To obtain clean surfaces, procedures of the coating deposition and sample joining are performed in situ in a vacuum of l0-4 Pa. The strength of the obtained joints is about 20MPa for indium coatings and about 30MPa for lead coatings. It is supposed that attractive surface forces play a decisive role in the contact formation and bonding of the wafers. The method has been applied for…

Drilling Systems: Stability and Hidden Oscillations

2013

There are many mathematical models of drilling systems Despite, huge efforts in constructing models that would allow for precise analysis, drilling systems, still experience breakdowns. Due to complexity of systems, engineers mostly use numerical analysis, which may lead to unreliable results. Nowadays, advances in computer engineering allow for simulations of complex dynamical systems in order to obtain information on the behavior of their trajectories. However, this simple approach based on construction of trajectories using numerical integration of differential equations describing dynamical systems turned out to be quite limited for investigation of stability and oscillations of these s…

Stochastic analysis of external and parametric dynamical systems under sub-Gaussian Levy white-noise

2008

In this study stochastic analysis of non-linear dynamical systems under α-stable, multiplicative white noise has been conducted. The analysis has dealt with a special class of α-stable stochastic processes namely sub-Gaussian white noises. In this setting the governing equation either of the probability density function or of the characteristic function of the dynamical response may be obtained considering the dynamical system forced by a Gaussian white noise with an uncertain factor with α/2- stable distribution. This consideration yields the probability density function or the characteristic function of the response by means of a simple integral involving the probability density function …

Qualitative Theory of Differential Equations, Difference Equations, and Dynamic Equations on Time Scales

2016

We are pleased to present this special issue. This volume reflects an increasing interest in the analysis of qualitative behavior of solutions to differential equations, difference equations, and dynamic equations on time scales. Numerous applications arising in the engineering and natural sciences call for the development of new efficient methods and for the modification and refinement of known techniques that should be adjusted for the analysis of new classes of problems. The twofold goal of this special issue is to reflect both the state-of-the-art theoretical research and important recent advances in the solution of applied problems.

OLS Identification of network topologies

2011

Abstract In many applications, it is important to derive information about the topology and the internal connections of more dynamical systems interacting together. Examples can be found in fields as diverse as Economics, Neuroscience and Biochemistry. The paper deals with the problem of deriving a descriptive model of a network, collecting the node outputs as time series with no use of a priori insight on the topology. We cast the problem as the optimization of a cost function where a set of parameters are used to operate a trade-off between accuracy and complexity in the final model. The problem of reducing the complexity is addressed by fixing a certain degree of sparsity and finding the…

On attracting sets in artificial networks: cross activation

2018

Mathematical models of artificial networks can be formulated in terms of dynamical systems describing the behaviour of a network over time. The interrelation between nodes (elements) of a network is encoded in the regulatory matrix. We consider a system of ordinary differential equations that describes in particular also genomic regulatory networks (GRN) and contains a sigmoidal function. The results are presented on attractors of such systems for a particular case of cross activation. The regulatory matrix is then of particular form consisting of unit entries everywhere except the main diagonal. We show that such a system can have not more than three critical points. At least n–1 eigenvalu…