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On the Dynamics of the Chaotic General Lorenz System
International Journal of Bifurcation and Chaos, 2017In this paper, the global attractive sets of the general Lorenz system are studied based on the Lyapunov stability theory and optimization theory. The innovation of this paper lies in that the method of constructing Lyapunov functions applied to many other dynamical systems is not applicable to this general Lorenz system.
Fuchen Zhang +4 more
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Multistability in the Lorenz System: A Broken Butterfly
International Journal of Bifurcation and Chaos, 2014In this paper, the dynamical behavior of the Lorenz system is examined in a previously unexplored region of parameter space, in particular, where r is zero and b is negative. For certain values of the parameters, the classic butterfly attractor is broken into a symmetric pair of strange attractors, or it shrinks into a small attractor basin ...
Chunbiao Li, Julien Clinton Sprott
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A class of Lorenz-like systems
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2012The transformation of a three-dimensional dynamical system to its differential model can be used to identify different nonlinear dynamical systems that share the same time series of one of its variables. This transformation then can be used to find classes of nonlinear dynamical systems with similar dynamical behavior.
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Phase synchronization in the forced Lorenz system
Physical Review E, 1999We demonstrate that the dynamics of phase synchronization in a chaotic system under weak periodic forcing depends crucially on the distribution of intrinsic characteristic times of this system. Under the external periodic action, the frequency of every unstable periodic orbit is locked to the frequency of the force.
Park, Eun Hyoung +2 more
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Lorenz-like systems and Lorenz-like attractors: Definition, examples, and equivalences
Physical Review E, 2023Since the early 1970s, numerous systems exhibiting an algebraic structure resembling that of the 1963 Lorenz system have been proposed. These systems have occasionally yielded the same attractor as the Lorenz system, while in other cases, they have not.
Christophe Letellier +2 more
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Linear response of the Lorenz system
Physical Review E, 2002The present numerical study provides strong evidence that at standard parameters the response of the Lorenz system to small perturbations of the control parameter r is linear. This evidence is obtained not only directly by determining the response in the observable A(x)=z, but also indirectly by validating various implications of the assumption of a ...
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Physics Letters A, 1993
Abstract A quotient of the Lorenz dynamical system is constructed. This “proto-Lorenz” system has the Lorenz system as a double covering, and the double covering explains the two-eared nature of the strange attractor for the Lorenz system. Arbitrary coverings of the proto-Lorenz system are possible, leading to n -eared strange attractors.
Rick Miranda, Emily Stone
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Abstract A quotient of the Lorenz dynamical system is constructed. This “proto-Lorenz” system has the Lorenz system as a double covering, and the double covering explains the two-eared nature of the strange attractor for the Lorenz system. Arbitrary coverings of the proto-Lorenz system are possible, leading to n -eared strange attractors.
Rick Miranda, Emily Stone
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Controlling The Lorenz System With Delay
2008A generalized method for adaptive control, synchronization of chaos and parameter identification in systems governed by ordinary differential equations and delay-differential equations is developed. The method is based on the Lagrangian approach to fluid dynamics.
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SHILNIKOV CHAOS IN LORENZ-LIKE SYSTEMS
International Journal of Bifurcation and Chaos, 2013For Lorenz-like system, conditions of Shilnikov chaos are obtained. Algorithms for computation of bifurcational values of parameters, which correspond to homoclinic trajectories are formulated. Modified Lorenz, Chen and Lu systems are considered.
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