0392923 20240111140831.520140304235959.9 10.1007/978-3-319-00542-3_31 8 s. P cav_un_epca*0392920978-3-319-00541-62194-5357210Advances In Intelligent Systems and Computing305-312ChamSpringer2013ZelinkaI.ChenG.RosslerO. E.SnášelV.AbrahamA. chaotic dynamical system Lorenz system Chen system cav_un_auth*0259382 Augustová Petra Teorie řízení Department of Control Theory TŘ TR UTIA-B Department of Control Theory Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0101066 Beran Zdeněk Teorie řízení Department of Control Theory TŘ TR UTIA-B Department of Control Theory Ústav teorie informace a automatizace AV ČR, v. v. i. textový dokument 506 kB GA13-20433S GA ČR cav_un_auth*0292613 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 famous Lorenz attractor. First, the integrals of motion are derived for some parameters of the Chen system. The integrals of motions play an important role in physics, e.g. for conservation laws. Next, the shape of the global attractor of this system is approximated by volumes that contain the attractor. The shape predicts the future behavior of the system. To obtain these results, the already proved fact that the Chen system is a continued transition of the Lorenz system is used. According to our knowledge, the same approach of shifting the known facts about the Lorenz system to a newdynamical system, the Chen system in this context, has not been presented yet. cav_un_auth*0291709 Nostradamus 2013 Ostrava 03.06.2013-05.06.2013 CZ 2014 BC 2 PR RVO:67985556 http://hdl.handle.net/11104/0221979 S 2013 textový dokument 506 kB cav_un_epca*0392920 Nostradamus 2013: Prediction, Modeling and Analysis of Complex Systems Advances In Intelligent Systems and Computing 210 978-3-319-00541-6 2194-5357 305 312 Cham Springer 2013 Zelinka I. 340 Chen G. 340 Rossler O. E. 340 Snášel V. 340 Abraham A. 340