Improving the Complexity of the Lorenz Dynamics
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...
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2017/3204073 |
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| _version_ | 1832559464621801472 |
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| author | María Pilar Mareca Borja Bordel |
| author_facet | María Pilar Mareca Borja Bordel |
| author_sort | María Pilar Mareca |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-0a3180c5418047e79046ad2622e80ec6 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-0a3180c5418047e79046ad2622e80ec62025-02-03T01:29:56ZengWileyComplexity1076-27871099-05262017-01-01201710.1155/2017/32040733204073Improving the Complexity of the Lorenz DynamicsMaría Pilar Mareca0Borja Bordel1Department of Physic Electronics, Universidad Politécnica de Madrid, Avenida Complutense No. 30, 28040 Madrid, SpainDepartment of Physic Electronics, Universidad Politécnica de Madrid, Avenida Complutense No. 30, 28040 Madrid, SpainA 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.http://dx.doi.org/10.1155/2017/3204073 |
| spellingShingle | María Pilar Mareca Borja Bordel Improving the Complexity of the Lorenz Dynamics Complexity |
| title | Improving the Complexity of the Lorenz Dynamics |
| title_full | Improving the Complexity of the Lorenz Dynamics |
| title_fullStr | Improving the Complexity of the Lorenz Dynamics |
| title_full_unstemmed | Improving the Complexity of the Lorenz Dynamics |
| title_short | Improving the Complexity of the Lorenz Dynamics |
| title_sort | improving the complexity of the lorenz dynamics |
| url | http://dx.doi.org/10.1155/2017/3204073 |
| work_keys_str_mv | AT mariapilarmareca improvingthecomplexityofthelorenzdynamics AT borjabordel improvingthecomplexityofthelorenzdynamics |