The purpose of this article is to provide an elementary introduction to the subject of chaos in the electromechanical drive systems with small MPTPRS. In this article, we explore chaotic solutions of maps and continuous time systems. These solutions are also bounded like equilibrium, periodic and quasiperiodic solutions. and POZOR! Nadpis obsahuje dvě chyby (překlepy - správně je: electromechanical (tj. vypustit chybné n) + systems (tj. vypustit druhé chybné s)
We focus on the special type of the continuous dynamical system which is genWe focus on the special type of the continuous dynamical system which is generated by Euler equation branching. Euler equation branching is a type of differential inclusion ˙x ∈ {f(x), g(x)}, where f, g : X ⊂ ℝ n → ℝ n are continuous and f(x) ≠ g(x) at every point x ∈ X. It seems this chaotic behaviour is typical for such dynamical system. In the second part we show an application in a new formulated overall macroeconomic equilibrium model. This new model is based on the fundamental macroeconomic aggregate equilibrium model called the IS-LM model.
Non-linearity is essential for occurrence of chaos in dynamical system. The size of phase space and formation of attractors are much dependent on the setting of nonlinear function and parameters. In this paper, a three-variable dynamical system is controlled by different nonlinear function thus a class of chaotic system is presented, the Hamilton function is calculated to find the statistical dynamical property of the improved dynamical systems composed of hidden attractors. The standard dynamical analysis is confirmed in numerical studies, and the dependence of attractors and Hamilton energy on non-linearity selection is discussed. It is found that lower average Hamilton energy can be detected when intensity of nonlinear function is enhanced. It indicates that non-linearity can decrease the energy cost triggering for dynamical behaviors.
In this paper, dual synchronization of a hybrid system containing a chaotic Colpitts circuit and a Chua's circuit, connected by an additive white Gaussian noise (AWGN) channel, is studied via numeric simulations. The extended Kalman filter (EKF) is employed as the response system to achieve the dual synchronization. Two methods are proposed and investigated. The first method treats the combination of a Colpitts circuit and a Chua's circuit as a higher-dimensional system, while the second method considers the Colpitts circuit and Chua's circuit separately and utilizes the cross-coupling scheme. The simulation results indicate that the proposed methods can effectively achieve and maintain dual synchronization of the hybrid system through an AWGN channel.
Chaos can be defined on bounded-state behaviour that is not equilibrium solution or a periodic solution or a quasiperiodic solution. The article is focused on analysis of dynamic properties of controlled drive systems and also on bifurcation of steady states and possible occurrence of chaotic behaviour. The purpose of this article is to provide an elementary introduction to the subject of chaos in the electromechanical drive systems. In this article, we explore chaotic solutions of maps and continuous time systems. The attractor associated with chaotic motion in state space is not a simple geometrical object like a finite number of points, a closed curve or a torus. Chaotic attractor is complex geometrical object that posses fractal dimensions. and Obsahuje seznam literatury
Finding sufficient criteria for synchronization of master-slave chaotic systems by replacing variables control has been an open problem in the field of chaos control. This paper presents some recent works on the subject, with emphasis on chaos synchronization of both identical and parametrically mismatched Lur'e systems by replacing variables control. The synchronization schemes are formally constructed and two classes of sufficient criteria for global synchronization, linear matrix inequality criterion and frequency-domain criterion, are reviewed and discussed.
Slovem chaos byl ve fyzice pojmenován obor, který se v rámci klasické mechaniky zabývá důsledky citlivé závislosti chování fyzikálních systémů na počátečních podmínkách, tedy tzv. efektem motýlích křídel. Jak ale popsat chaotické chování ve světě kvantových částic? Ukazuje se, že kvantová mechanika citlivou závislost na počátečních podmínkách nepřipouští, a navíc předpovídá podstatné potlačení chaosu i na makroskopické úrovni. Přesto se kvantové vlastnosti systémů, které jsou podle klasické mechaniky chaotické, zásadně liší od vlastností klasicky uspořádaných systémů. Studiem těchto otázek se zabývá obor označovaný jako kvantový chaos., Pavel Cejnar., Součástí obr. simulace stáčení magnetizace... na str. 267, and Obsahuje seznam literatury
In the paper, a possible characterization of a chaotic behavior for the generalized semiflows in finite time is presented. As a main result, it is proven 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. A connection with symbolic dynamical systems is mentioned and a possible numerical method of analysis of dynamical behavior is outlined.
The biped robot with flat feet and fixed ankles walking down a slope is a typical impulsive dynamic system. Steady passive gaits for such mechanism can be induced on certain shallow slopes without actuation. The steady gaits can be described by using stable non-smooth limit cycles in phase plane. In this paper, it is shown that the robot gaits are affected by three parameters, namely the ground slope, the length of the foot, and the mass ratio of the robot. As the ground slope is gradually increased, the gaits exhibit universal period doubling bifurcations leading to chaos. Meanwhile, the phenomena of period doubling bifurcations also occur by increasing either the foot length or the mass ratio of the robot. Theory analysis and numerical simulations are given to verify our conclusion.
Volně se vznášející balvany, oheň, v pozadí moře a sloup kouře., Karner 2007#, 134, and Součást cyklu 16 výjevů z Ovidiových Proměn shrnující historii vesmíru, které jsou seřazeny tak, jak po sobě následují v literární předloze. V jednotlivých klenebních polích jsou výjevy uspořádány v osmi kontrastních párech, které začínají chaosem, proti němuž je postaven uspořádaný svět.