Improving the complexity of the Lorenz dynamics
type: Item
instance of: scholarly article
title: Improving the complexity of the Lorenz dynamics
zbMATH Open document ID: 1367.34062
DOI: 10.1155/2017/3204073
author: María Pilar Mareca
author: Borja Bordel
published in: Complexity
publication date: 2017-08-03T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 34C60
Mathematics Subject Classification ID: 37D45
zbMATH DE Number: 6755967
zbMATH Keywords: four-dimensional hyperchaotic dynamic system
zbMATH Keywords: Lorenz dynamics
zbMATH Keywords: chaotic dissipative flows
zbMATH Keywords: first return maps
zbMATH Keywords: Poincaré cross sections
zbMATH Keywords: Lyapunov spectrum
zbMATH Keywords: bifurcation diagrams
zbMATH Keywords: Kaplan-Yorke dimension
Wikidata QID: Q58804352
describes a project that uses: CyPhySim
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2017/3204073
OpenAlex ID: W2570533536
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DBLP publication ID: journals/complexity/MarecaB17
description: scientific article; zbMATH DE number 6755967