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Synchronization in the Lorenz system

, 2016
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DYNAMICS OF A SIMPLIFIED LORENZ SYSTEM

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 2009
A simplified Lorenz system with one bifurcation parameter is investigated by a detailed theoretical analysis as well as dynamic simulation, including some basic dynamical properties, Lyapunov exponent spectra, fractal dimension, bifurcations and routes to chaos. The results show that this system has complex dynamics with interesting characteristics.
J C Sprott, Kehui Sun
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Linearization of the Lorenz system

Physics Letters, Section A: General, Atomic and Solid State Physics, 2015
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
J C Sprott, Chunbiao Li
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Lagrangian Formulation of Lorenz and Chen Systems

International Journal of Bifurcation and Chaos, 2021
This paper presents the formulation of Lagrangian function for Lorenz, Modified Lorenz and Chen systems using Lagrangian functions depending on fractional derivatives of differentiable functions, and the estimation of the conserved quantity associated with the respective systems.
Palanisamy Vijayalakshmi, Zhiheng Jiang, Xiong Wang   +2 more
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Multifractality of the Lorenz system

Physical Review E, 1996
We use the unstable periodic orbit expansion of the dynamical \ensuremath{\zeta} function to find the multifractal spectra f(\ensuremath{\alpha}) and g(\ensuremath{\Lambda}) for the Lorenz system at (r,\ensuremath{\sigma},b)=(28,10,8/3) and also for an incomplete, generalized Baker's map with the topology of the Lorenz system. \textcopyright{} 1996 The
, Wiklund, , Elgin
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THE POINTWISE COMPUTABILITY OF THE LORENZ SYSTEM

Mathematical Models and Methods in Applied Sciences, 1998
We give evidence that most trajectories of the Lorenz system of ordinary differential equations are pointwise computable on time intervals of moderate length using an adaptive finite element method. Based on accurate computation, we present a description of the structure of the solutions of the Lorenz system as a repeated process of cutting-expanding ...
Estep, Don, Johnson, Claes
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On the Feedback Linearization of the Lorenz System

Journal of Vibration and Control, 2004
In this paper we present a control study of the Lorenz system via feedback linearization using the Rayleigh number as a control variable. The effects of the state transformation on the dynamics of the system are studied first. Then, composite controls are derived for both stabilization and tracking problems.
Crespo, L. G., Sun, J. Q.
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On Lorenz and Chen Systems

International Journal of Bifurcation and Chaos, 2018
In this work, a simple comparative analysis on the Lorenz and the Chen systems is presented, in order to understand some aspects that make these two systems distinct from one another.
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Boundedness of a Class of Complex Lorenz Systems

International Journal of Bifurcation and Chaos, 2021
The estimate of the ultimate bound for a dynamical system is an important problem, which is useful for chaos control and synchronization. In this paper, the estimated ultimate bound of a class of complex Lorenz systems is provided, which extends the parameter regions identified in the current literature on this problem.
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DYNAMICS OF A HYPERCHAOTIC LORENZ SYSTEM

International Journal of Bifurcation and Chaos, 2007
In this paper, we investigate the dynamics of the Lorenz system, linearly extended into one additional dimension. The system is hyperchaotic in a wide range of parameters. A theoretical and numerical study indicates that chaos and hyperchaos are produced with the help of a van der Pol-like oscillatory motion around a hypersaddle stationary point at ...
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