On the generalized Lorenz canonical form

“…In 2002, Lü found another new critical chaotic system [19]. These systems can be included in the following generalized Lorenz system [20] which is described bẏ…”

Section: Illustrative Examplementioning

confidence: 99%

Hybrid Synchronization of Uncertain Generalized Lorenz System by Adaptive Control

Zhou

2018

Journal of Control Science and Engineering

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This paper investigates hybrid synchronization of the uncertain generalized Lorenz system. Several useful criteria are given for synchronization of two generalized Lorenz systems, and the adaptive control law and the parameter update law are used. In comparison with those of existing synchronization methods, hybrid synchronization includes full-order synchronization, reduced-order synchronization, and modified projective synchronization. What is more, control of the stability point, complete synchronization, and antisynchronization can coexist in the same system. Numerical simulations show the effectiveness of this method in a class of chaotic systems.

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“…If In this case, system (6) has five equilibria (including the zero equilibrium). It means system (6) is not topologically equivalent to the generalized Lorenz canonical form (GLCF) [20] which have three-equilibria at most.…”

Section: Equlibriamentioning

confidence: 99%

“…Recently some new chaotic systems were proposed, including the Chen system, the generalized Lorenz system family, and the hyperbolic-type of generalized Lorenz canonical form [18][19][20]. Some four-dimensional chaotic systems were also presented, which have more complicated dynamic properties than three-dimensional chaotic systems, such as the system proposed in [21].…”

Section: Introductionmentioning

confidence: 99%

A 3-D four-wing attractor and its analysis

Wang¹,

Sun²,

Wyk³

et al. 2009

Braz. J. Phys.

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In this paper, several three dimensional (3-D) four-wing smooth quadratic autonomous chaotic systems are analyzed. It is shown that these systems have a number of similar features. A new 3-D continuous autonomous system is proposed based on these features. The new system can generate a four-wing chaotic attractor with less terms in the system equations. Several basic properties of the new system is analyzed by means of Lyapunov exponents, bifurcation diagrams and Poincare maps. Phase diagrams show that the equilibria are related to the existence of multiple wings.

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On the generalized Lorenz canonical form

Cited by 149 publications

References 16 publications

Finite-time synchronization of chaotic systems with noise perturbation

Finite-time synchronization of chaotic systems with noise perturbation

Hybrid Synchronization of Uncertain Generalized Lorenz System by Adaptive Control

A 3-D four-wing attractor and its analysis

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