A New Category of Three-Dimensional ChaoticFlows with Identical Eigenvalues

Zahra Faghani and Fahimeh Nazarimehr
Biomedical Engineering Department,
Amirkabir University of Technology,
Tehran 15875-4413, Iran
Sajad Jafari∗
Nonlinear Systems and Applications,
Faculty of Electrical and Electronics Engineering,
Ton Duc Thang University, Ho Chi Minh City, Vietnam
sajad.jafari@tdtu.edu.vn
Julien C. Sprott
Department of Physics, University of Wisconsin,
Madison, WI 53706, USA

Received March 8, 2019; Revised June 24, 2019

In this paper, some new three-dimensional chaotic systems are proposed. The special property of these autonomous systems is their identical eigenvalues. The systems are designed based on the general form of quadratic jerk systems with 10 terms, and some systems with stable equilibria. Using a systematic computer search, 12 simple chaotic systems with identical eigenvalues were found. We believe that systems with identical eigenvalues are described here for the first time. These simple systems are listed in this paper, and their dynamical properties are investigated.

Ref: Z. Faghani, F. Nazarimehr, S. Jafari, and J. C. Sprott, International Journal of Bifurcation and Chaos 30, 2050026-1-9 (2020)

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