Bifurcation schemes of the Lorenz model

Impulsive Control and Synchronization of Complex Lorenz Systems

“…Our interest in the present paper is to study the impulsive control and synchronization of chaotic attractors of the complex Lorenz system (5). This study can be considered as a continuation of our studies in the literature for complex Lorenz systems.…”

“…In the last 30 years, chaotic systems involving both real and complex variables governed by complex ordinary differential equations have been widely studied and investigated which contain one or more complex variables that make multiplication of variables that appear in many important applications in engineering; for example, in communications, where doubling the number of variables may be used to increase the content and security of the transmitted information, used to describe and simulate the physics of detuned laser and thermal convection of liquid flows, the electric field amplitude and the atomic polarization amplitude are both complex (see [1][2][3][4][5]).…”

Bursting phenomena as well as the bifurcation mechanism in controlled Lorenz oscillator with two time scales

“…It is found that three equilibrium points may exist in the system, the properties of which change with the variation of the parameters, while the trajectory of the system cycling around two foci may form a chaotic attractor as butterfly [5,6]. Obviously, from an implementation point of view, chaotic systems with simpler structures deserve more attention, for which 3D autonomous systems are of the lowest possible dimensions.…”

High-Dimensional Chaos in Dissipative and Driven Dynamical Systems

“…The Lorenz model has been extensively studied in the literature (e.g., Sparrow 1982;Schmutz & Rueff 1984;Thompson & Stewart 1986;Jackson 1990; Argyris et al 1993); its importance is that it shows a variety of phenomena typical for 3D dissipative and driven dynamical systems, and that it was the first system in which a strange (chaotic) attractor was discovered (Lorenz 1963).…”

“…Extensive studies of the Lorenz model (e.g., Lorenz 1963Lorenz , 1984Sparrow 1982Sparrow , 1986Schmutz & Rueff 1984;Thompson & Stewart 1986;Argyris et al 1993) showed that at r = 24.75 the system exhibits fully developed chaos and the Lorenz chaotic (strange) attractor is formed (see Fig. 1).…”