Eur. Phys. J. B (2013) 86: 394
https://doi.org/10.1140/epjb/e2013-40532-2

Regular Article

On the transition to hyperchaos and the structure of hyperchaotic attractors

¹ Department of Physics, The Cochin College, 682002 Cochin, India
² Inter University Centre for Astronomy and Astrophysics, 411007 Pune, India
³ Indian Institute of Science Education and Research, 411021 Pune, India

^a e-mail: kphk2002@yahoo.co.in

Received: 28 May 2013
Received in final form: 6 July 2013
Published online: 23 September 2013

Abstract

Using a recently proposed algorithmic scheme for correlation dimension analysis of hyperchaotic attractors, we study two well-known hyperchaotic flows and two standard time delayed hyperchaotic systems in detail numerically. We show that at the transition to hyperchaos, the nature of the scaling region changes suddenly and the attractor displays two scaling regions for embedding dimension M ≥ 4. We argue that it is an indication of a strong clustering tendency of the underlying attractor in the hyperchaotic phase. Because of this sudden qualitative change in the scaling region, the transition to hyperchaos can be easily identified using the discontinuous changes in the dimension (D₂) at the transition point. We show this explicitely for the two time delayed systems. Further support for our results is provided by computing the spectrum of Lyapunov Exponents (LE) of the hyperchaotic attractor in all cases. Our numerical results imply that the structure of a hyperchaotic attractor is topologically different from that of a chaotic attractor with inherent dual scales, at least for the two general classes of hyperchaotic systems we have analysed here.