0399907 20240111140838.420131218235959.9 000325824900025 84886290240 10.1007/s11071-013-1007-4 12 s. E cav_un_epca*02545250924-090X743 (2013)819-830 Chaotic behavior Lyapunov exponent Bifurcation parameter Bifurcation diagram Stability analysis cav_un_auth*0297166 García-Martínez M. MX cav_un_auth*0297167 Campos-Cantón I. MX cav_un_auth*0295508 Campos-Cantón E. MX cav_un_auth*0101074 Čelikovský Sergej 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 http://library.utia.cas.cz/separaty/2013/TR/celikovsky-0399907.pdf http://link.springer.com/article/10.1007/s11071-013-1007-4 811 KB GA13-20433S GA ČR cav_un_auth*0292613 In this paper we study the dynamical behavior of the one-dimensional discrete-time system, the so-called iterated map. Namely, a bimodal quadratic map is introduced which is obtained as an amplification of the difference between well-known logistic and tent maps. Thus, it is denoted as the so-called difference map. The difference map exhibits a variety of behaviors according to the selection of the bifurcation parameter. The corresponding bifurcations are studied by numerical simulations and experimentally. The stability of the difference map is studied by means of Lyapunov exponent and is proved to be chaotic according to Devaney’s definition of chaos. Later on, a design of the electronic implementation of the difference map is presented. The difference map electronic circuit is built using operational amplifiers, resistors and an analog multiplier. It turns out that this electronic circuit presents fixed points, periodicity, chaos and intermittency that match with high accuracy to the corresponding values predicted theoretically. 2014 BC 4 4 A 4a 20231122135941.9 RVO:67985556 http://hdl.handle.net/11104/0227921 ENGINEERINGMECHANICAL|MECHANICS 2.424 0.482 3.IX 0.01284 0.553 5603 407 1.203 Q1 40.264 90.559 Q3 Q1 2013 Soubory v repozitáři: celikovsky-0399907.pdf 84886290240 SCOPUS 000325824900025 WOS textový dokument 811 KB cav_un_epca*0254525 Nonlinear Dynamics 0924-090X 1573-269X Roč. 74 č. 3 2013 819 830