Synchronization and Impulsive Control of Some Parabolic Partial Differential Equations
American Journal of Theoretical and Applied Statistics
Volume 6, Issue 5-1, September 2017, Pages: 30-39
Received: Mar. 7, 2017; Accepted: Mar. 8, 2017; Published: Apr. 5, 2017
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Authors
Mahmoud M. El-Borai, Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, Alexandria, Egypt
Wagdy G. Elsayed, Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, Alexandria, Egypt
Turkiya Alhadi Aljamal, Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, Alexandria, Egypt
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Abstract
Novel equi-attractivity in large generalized non-linear partial differential equations were performed for the impulsive control of spatiotemporal chaotic. Attractive solutions of these general partial differential equations were determined. A proof for existence of a certain kind of impulses for synchronization such that the small error dynamics that is equi-attractive in the large is established. A comparative study between these general non-linear partial differential equations and the existent reported numerical theoretical models was developed. Several boundary conditions were given to confirm the theoretical results of the general non-linear partial differential equations. Moreover, the equations were applied to Kuramoto–Sivashinsky PDE′s equation; Grey–Scott models, and Lyapunov exponents for stabilization of the large chaotic systems with elimination of the dynamic error.
Keywords
Synchronization, Impulsive Control, Prabolic Partial Differential Equations
To cite this article
Mahmoud M. El-Borai, Wagdy G. Elsayed, Turkiya Alhadi Aljamal, Synchronization and Impulsive Control of Some Parabolic Partial Differential Equations, American Journal of Theoretical and Applied Statistics. Special Issue: Statistical Distributions and Modeling in Applied Mathematics. Vol. 6, No. 5-1, 2017, pp. 30-39. doi: 10.11648/j.ajtas.s.2017060501.15
Copyright
Copyright © 2017 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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