Zdenek Beran

• PhD
• Research Associate at The Czech Academy of Sciences

The aim of this paper is to present the application of the analytical series technique to study properties of the nonlinear chaotic dynamical systems. More specifically, Laplace–Adomian decomposition method is applied to Rössler system and the so-called generalized Lorenz system. Some advantages and possible applications of this approach are discus...

: Experimental numerical analysis of the analytical series technique to solve nonlinear systems based on the so-called Adomian polynomials expansions will be presented here. Unlike standard difference methods like Runge-Kutta schemes of various orders, the Adomian method enables to compute a single approximation on relatively long time intervals. T...

The main aim of this paper is to demonstrate a possible risk of erroneous conclusions made throughout the process of the sampled data analysis. In particular, it will be shown that the false chaotic behavior of the sampled data may be incorrectly derived from the topo-logical similarity with the already well known chaotic systems like that of Loren...

The application of the functional derivatives to the mathematical modeling of complex systems is studied here. The connection of functional derivatives with total differentials in Banach spaces is shown. Local and global existence theorems for the linear equations in total differentials are proved. Consequently, a total integrability conditions are...

Within the paper a mathematical representation of the so-called Chen model is described as a particular parametric three-dimensional chaotic dynamical system, i.e. a system of three nonlinear differential equations evolving in time. The main aim of this paper is to find for the Chen system the properties that are known for the Lorenz system and its...

In this paper, the chaotic behavior of a set-valued mapping F : X → 2X, where X is a compact space, is investigated. The existence of the generalized shadowing property in the hyperspace 2X is proved. Based on the generalized shadowing property of the set-valued mappings F and the assumption of the existence of an unstable chain recurrent point of...

This contribution addresses a possible description of the chaotic behavior in multivalued dynamical systems. For the multivalued system formulated via differential inclusion the practical conditions on the right-hand side are derived to guarantee existence of a solution, which leads to the chaotic behavior. Our approach uses the notion of the gener...

This contribution addresses a possible description of the chaotic behavior in multi-valued dynamical systems. An important area leading to description via the multi-valued dynamical systems is the non-smooth dy-namical systems theory and their applications. Examples of such applications are mechanics with dry friction , electric circuits with small...

A possible characterization of a chaotic behavior for the generalized semiflows in finite time is presented. As a main result, it is proved that under specific conditions there is at least one trajectory of generalized semiflow, which lies inside an arbitrary covering of the solution set. The trajectory mutually connects each subset of the covering...

Multi-spectral fusion focused on the task of image enhancement by processing raw data collected at various electromagnetic bands via passive sensors. Passive spectral sensors collect information about the scene based on the inherently reflected or emitted energy of the scene and is represented by spectral distributions and intensities. These system...

The experimental equipment with LD anemometry for the research of suspension flow in a horizontal pipeline is described. Presented results consist of velocity profiles for liquid phase and moving solid particles, intensity of turbulence of longitudinal velocity components, some velocity histograms, energy spectrum functions and Euler correlations o...

For the solution of certain optimal control problems with elliptic systems and inequality state-space constraints the augmented Lagrangian approach is proposed. In order to ensure the existence of a solution of the appropriate dual problem, special class of augmented Lagrangians is constructed on such Sobolev spaces for which the continuous imbeddi...

A simple approach is proposed to find a suitable discrete description of the continuously varying system. An optimization problem is solved for the approximation of linear operators on the class of function exhibiting certain smoothness properties. More exactly, a general method determining approximate derivatives is suggested which exploits only f...