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Complexity
Volume 2017, Article ID 3204073, 16 pages
https://doi.org/10.1155/2017/3204073
Research Article

Improving the Complexity of the Lorenz Dynamics

Department of Physic Electronics, Universidad Politécnica de Madrid, Avenida Complutense No. 30, 28040 Madrid, Spain

Correspondence should be addressed to María Pilar Mareca; se.mpu.sif@acerampm

Received 26 July 2016; Accepted 19 September 2016; Published 10 January 2017

Academic Editor: Michael Small

Copyright © 2017 María Pilar Mareca and Borja Bordel. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A new four-dimensional, hyperchaotic dynamic system, based on Lorenz dynamics, is presented. Besides, the most representative dynamics which may be found in this new system are located in the phase space and are analyzed here. The new system is especially designed to improve the complexity of Lorenz dynamics, which, despite being a paradigm to understand the chaotic dissipative flows, is a very simple example and shows great vulnerability when used in secure communications. Here, we demonstrate the vulnerability of the Lorenz system in a general way. The proposed 4D system increases the complexity of the Lorenz dynamics. The trajectories of the novel system include structures going from chaos to hyperchaos and chaotic-transient solutions. The symmetry and the stability of the proposed system are also studied. First return maps, Poincaré sections, and bifurcation diagrams allow characterizing the global system behavior and locating some coexisting structures. Numerical results about the first return maps, Poincaré cross sections, Lyapunov spectrum, and Kaplan-Yorke dimension demonstrate the complexity of the proposed equations.