Improving the complexity of Lorenz dynamics

Mareca López, María Pilar and Bordel Sánchez, Borja (2017). Improving the complexity of Lorenz dynamics. "Complexity", v. 2017 (n. 320407); pp. 1-16. ISSN 1076-2787.


Title: Improving the complexity of Lorenz dynamics
  • Mareca López, María Pilar
  • Bordel Sánchez, Borja
Item Type: Article
Título de Revista/Publicación: Complexity
Date: 10 January 2017
ISSN: 1076-2787
Volume: 2017
Faculty: E.T.S.I. Telecomunicación (UPM)
Department: Electrónica Física
Creative Commons Licenses: Recognition - No derivative works - Non commercial

Full text

PDF - Requires a PDF viewer, such as GSview, Xpdf or Adobe Acrobat Reader
Download (4MB) | Preview


A new four-dimensional, hyperchaotic dynamic system, based on Lorenz dynamics, is presented. Besides, the most representative dynamics whichmay 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.

Funding Projects

Government of SpainFPU15/03977FPU ProgramUnspecifiedUnspecified
Government of SpainTEC2015-68284-RSEMOLAUnspecifiedUnspecified
Madrid Regional GovernmentP2013/ICE-3019MOSI-AGIL-CMUnspecifiedUnspecified

More information

Item ID: 52969
DC Identifier:
OAI Identifier:
DOI: 10.1155/2017/3204073
Official URL:
Deposited by: Memoria Investigacion
Deposited on: 13 Nov 2018 15:53
Last Modified: 30 Nov 2022 09:00
  • Logo InvestigaM (UPM)
  • Logo GEOUP4
  • Logo Open Access
  • Open Access
  • Logo Sherpa/Romeo
    Check whether the anglo-saxon journal in which you have published an article allows you to also publish it under open access.
  • Logo Dulcinea
    Check whether the spanish journal in which you have published an article allows you to also publish it under open access.
  • Logo de Recolecta
  • Logo del Observatorio I+D+i UPM
  • Logo de OpenCourseWare UPM