Estimation of Lyapunov dimension for the Chen and Lu systems

TL;DR

This paper revises previous estimates of Lyapunov dimension for Chen and Lu systems, correcting inaccuracies and clarifying the valid parameter domains, using reduction to the generalized Lorenz system and Leonov's method.

Contribution

It corrects earlier inaccuracies in Lyapunov dimension estimates for Chen and Lu systems and refines the valid parameter domains for these estimates.

Findings

Previous estimates contained inaccuracies.

Revised parameter domains exclude classical parameters.

Leonov's method was used for correction.

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.