Simple Chaotic 3D Flows with Surfaces of Equilibria

Sajad Jafari
Biomedical Engineering Department, Amirkabir University of Technology, Tehran 15875-4413, Iran

J. C. Sprott
Department of Physics, University of Wisconsin-Madison, Madison, WI 53706, USA

Viet-Thanh Pham
School of Electronics and Telecommunications, Hanoi University of Science and Technology, 01 Dai Co Viet, Hanoi, Vietnam

Chunbiao Li
Jiangsu Key Laboratory of Meteorological Observation and Information Processing, Nanjing University of Information Science and Technology, Nanjing 210044, China
School of Electronic and Information Engineering, Nanjing University of Information Science and Techology, Nanjing 210044, China

Received: 6 April 2016 / Accepted: 18 July 2016 / Published online: 27 July 2016

ABSTRACT

Using a systematic computer search, twelve simple three-dimensional chaotic flows were found that have surfaces of equilibria. Although there are some four-dimensional systems with surfaces of equilibria, there is no such system in three-dimensional state space reported in the literature. Such systems are not difficult to design, but they can have some practical benefits. Study of chaotic flows with surfaces of equilibria provides a good reference for building systems with attractors that are protected from external influences, which can increase the safety of engineering.

Ref: S. Jafari, J. C. Sprott, V. -T. Pham, C. Volos and C. Li, Nonlinear Dynamics 86, 1349-1358 (2016)