Estimation of Lyapunov dimension for the Chen and Lu systems

Abstract

Nowadays various estimates of Lyapunov dimension of Lorenz-like systems attractors are actively developed. Within the frame of this study the question arises whether it is possible to obtain the corresponding estimates of dimension for the Chen and Lu systems using the reduction of them to the generalized Lorenz system. In the work (Chen and Yang, 2013) Leonov's method was applied for the estimation of Lyapunov dimension, and as a consequence the Lyapunov dimension of attractors of the Chen and Lu systems with the classical parameters was estimated. In the present work an inaccuracy in (Chen and Yang, 2013) is corrected and it is shown that the revised domain of parameters, where the estimate of Lyapunov dimension is valid, does not involve the classical parameters of the Chen and Lu systems.

References in corpus (2)

• Differences and similarities in the analysis of Lorenz, Chen, and Lu systems
• Invariance of Lyapunov exponents and Lyapunov dimension for regular and irregular linearizations

Cited by in corpus (4)

• Homoclinic orbits, and self-excited and hidden attractors in a Lorenz-like system describing convective fluid motion
• The Lyapunov dimension and its estimation via the Leonov method
• The Lyapunov dimension formula for the global attractor of the Lorenz system
• Lyapunov dimension formula of attractors in the Tigan and Yang systems