Passivity-based chaos control and synchronization of the four dimensional Lorenz-Stenflo system via one input

Abstract

This paper discusses chaos control and synchronization of the four dimensional Lorenz-Stenflo system based on passive control technique. Using passive theory, chaos control and synchronization of a four dimensional Lorenz-Stenflo chaotic system are realized with one input. The designed controllers ensure the stability of the controlled system and error dynamical system between two identical Lorenz-Stenflo systems. Also, the controllers ensure that the controlled system and error dynamical system converge to zero equilibrium. Numerical simulations show that the proposed method is effective for the Lorenz-Stenflo system.

Synchronization of Vilnius Chaotic Oscillators With Active and Passive Control

“…0 and _ W ðzÞ 0, it can be concluded that W ðzÞ is the Lyapunov function of f 0 ðzÞ and that f 0 ðzÞ is globally asymptotically stable. 25 So, the zero dynamics of Vilnius chaotic system is stable with the Lyapunov's method. The controlled system can be equivalent to a passive system and globally asymptotically stabilized at its zero equilibrium by the following state feedback controller 24 :…”

“…Since the seminal work by Pecora and Carroll, the synchronization and control in chaotic systems have caught a lot of attention among scientists. Various techniques have been used for the synchronization of chaotic systems, such as active control, [17][18][19][20][21] passive control, [22][23][24][25] linear feedback control, 26 nonlinear control, 27 sliding mode control, 28 backstepping control, 21 impulsive control, 29 and so on. Synchronization using active control was introduced by Bai and Lonngren using Lorenz system in 1997 17 and later it has been implemented for the synchronization of other chaotic systems.…”

“…Synchronization using active control was introduced by Bai and Lonngren using Lorenz system in 1997 17 and later it has been implemented for the synchronization of other chaotic systems. [18][19][20][21] Besides, the synchronization using passive control was applied to Chen,22 Rikitake, 23 uni¯ed, 24 Lorenz-Sten°o, 25 and many other chaotic systems. Detailed information about the theory of active and passive control can be found in number of studies.…”

“…Detailed information about the theory of active and passive control can be found in number of studies. [17][18][19][20][21][22][23][24][25] Chaos synchronization and control have also been widely employed in a variety of¯elds including physics, chemistry, ecology, biological systems,¯nance and secure communication. 30,31 To the knowledge of the authors, the control of chaos in Vilnius oscillator is determined by using time-delay feedback controllers, 32 but no study has been carried out to synchronize the chaotic Vilnius oscillators.…”

Melnikov’s Criteria and Chaos Analysis in the Nonlinear Schrödinger Equation with Kerr Law Nonlinearity

“…In this paper, we will study the chaotic behavior and control of (1) under two-frequency perturbations. We study the bifurcation and dynamical behaviors depending on the parameters by using bifurcation and chaos theories in [15][16][17][18][19][20][21] and numerical simulation. By applying Melnikov method [15,20,21], we prove the criterion of existence of chaos under periodic perturbation.…”