Analysis and Adaptive Synchronization of Two Novel Chaotic Systems with Hyperbolic Sinusoidal and Cosinusoidal Nonlinearity and Unknown Parameters
This research work describes the modelling of two novel 3-D chaotic systems, the first with a hyperbolic sinusoidal nonlinearity and two quadratic nonlinearities (denoted as system (A)) and the second with a hyperbolic cosinusoidal nonlinearity and two quadratic nonlinearities (denoted as system (...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Eastern Macedonia and Thrace Institute of Technology
2013-09-01
|
| Series: | Journal of Engineering Science and Technology Review |
| Subjects: | |
| Online Access: | http://www.jestr.org/downloads/Volume6Issue4/fulltext7642013.pdf |
| _version_ | 1818201257250127872 |
|---|---|
| author | S. Vaidyanathan |
| author_facet | S. Vaidyanathan |
| author_sort | S. Vaidyanathan |
| collection | DOAJ |
| description | This research work describes the modelling of two novel 3-D chaotic systems, the first with a hyperbolic sinusoidal
nonlinearity and two quadratic nonlinearities (denoted as system (A)) and the second with a hyperbolic cosinusoidal
nonlinearity and two quadratic nonlinearities (denoted as system (B)). In this work, a detailed qualitative analysis of the
novel chaotic systems (A) and (B) has been presented, and the Lyapunov exponents and Kaplan-Yorke dimension of
these chaotic systems have been obtained. It is found that the maximal Lyapunov exponent (MLE) for the novel chaotic
systems (A) and (B) has a large value, viz. for the system (A) and for the system (B). Thus, both the novel chaotic
systems (A) and (B) display strong chaotic behaviour. This research work also discusses the problem of finding adaptive
controllers for the global chaos synchronization of identical chaotic systems (A), identical chaotic systems (B) and nonidentical chaotic systems (A) and (B) with unknown system parameters. The adaptive controllers for achieving global
chaos synchronization of the novel chaotic systems (A) and (B) have been derived using adaptive control theory and
Lyapunov stability theory. MATLAB simulations have been shown to illustrate the novel chaotic systems (A) and (B),
and also the adaptive synchronization results derived for the novel chaotic systems (A) and (B). |
| first_indexed | 2024-12-12T02:50:41Z |
| format | Article |
| id | doaj.art-1314a6d4474e4572867294754b7c3205 |
| institution | Directory Open Access Journal |
| issn | 1791-2377 1791-2377 |
| language | English |
| last_indexed | 2024-12-12T02:50:41Z |
| publishDate | 2013-09-01 |
| publisher | Eastern Macedonia and Thrace Institute of Technology |
| record_format | Article |
| series | Journal of Engineering Science and Technology Review |
| spelling | doaj.art-1314a6d4474e4572867294754b7c32052022-12-22T00:40:54ZengEastern Macedonia and Thrace Institute of TechnologyJournal of Engineering Science and Technology Review1791-23771791-23772013-09-01645365Analysis and Adaptive Synchronization of Two Novel Chaotic Systems with Hyperbolic Sinusoidal and Cosinusoidal Nonlinearity and Unknown ParametersS. Vaidyanathan0R & D Centre, Vel Tech University, 42, Avadi-Alamathi Road, Chennai-600 062, INDIAThis research work describes the modelling of two novel 3-D chaotic systems, the first with a hyperbolic sinusoidal nonlinearity and two quadratic nonlinearities (denoted as system (A)) and the second with a hyperbolic cosinusoidal nonlinearity and two quadratic nonlinearities (denoted as system (B)). In this work, a detailed qualitative analysis of the novel chaotic systems (A) and (B) has been presented, and the Lyapunov exponents and Kaplan-Yorke dimension of these chaotic systems have been obtained. It is found that the maximal Lyapunov exponent (MLE) for the novel chaotic systems (A) and (B) has a large value, viz. for the system (A) and for the system (B). Thus, both the novel chaotic systems (A) and (B) display strong chaotic behaviour. This research work also discusses the problem of finding adaptive controllers for the global chaos synchronization of identical chaotic systems (A), identical chaotic systems (B) and nonidentical chaotic systems (A) and (B) with unknown system parameters. The adaptive controllers for achieving global chaos synchronization of the novel chaotic systems (A) and (B) have been derived using adaptive control theory and Lyapunov stability theory. MATLAB simulations have been shown to illustrate the novel chaotic systems (A) and (B), and also the adaptive synchronization results derived for the novel chaotic systems (A) and (B).http://www.jestr.org/downloads/Volume6Issue4/fulltext7642013.pdfChaoschaotic attractorsLyapunov exponentssynchronizationadaptive control. |
| spellingShingle | S. Vaidyanathan Analysis and Adaptive Synchronization of Two Novel Chaotic Systems with Hyperbolic Sinusoidal and Cosinusoidal Nonlinearity and Unknown Parameters Journal of Engineering Science and Technology Review Chaos chaotic attractors Lyapunov exponents synchronization adaptive control. |
| title | Analysis and Adaptive Synchronization of Two Novel Chaotic Systems with Hyperbolic Sinusoidal and Cosinusoidal Nonlinearity and Unknown Parameters |
| title_full | Analysis and Adaptive Synchronization of Two Novel Chaotic Systems with Hyperbolic Sinusoidal and Cosinusoidal Nonlinearity and Unknown Parameters |
| title_fullStr | Analysis and Adaptive Synchronization of Two Novel Chaotic Systems with Hyperbolic Sinusoidal and Cosinusoidal Nonlinearity and Unknown Parameters |
| title_full_unstemmed | Analysis and Adaptive Synchronization of Two Novel Chaotic Systems with Hyperbolic Sinusoidal and Cosinusoidal Nonlinearity and Unknown Parameters |
| title_short | Analysis and Adaptive Synchronization of Two Novel Chaotic Systems with Hyperbolic Sinusoidal and Cosinusoidal Nonlinearity and Unknown Parameters |
| title_sort | analysis and adaptive synchronization of two novel chaotic systems with hyperbolic sinusoidal and cosinusoidal nonlinearity and unknown parameters |
| topic | Chaos chaotic attractors Lyapunov exponents synchronization adaptive control. |
| url | http://www.jestr.org/downloads/Volume6Issue4/fulltext7642013.pdf |
| work_keys_str_mv | AT svaidyanathan analysisandadaptivesynchronizationoftwonovelchaoticsystemswithhyperbolicsinusoidalandcosinusoidalnonlinearityandunknownparameters |