Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 723629, 11 pages
http://dx.doi.org/10.1155/2011/723629
Research Article

Numerical Integration and Synchronization for the 3-Dimensional Metriplectic Volterra System

Gheorghe Ivan,1 Mihai Ivan,1 and Camelia Pop2

1Seminarul de Geometrie şi Topologie, West University of Timişoara, 4, B-dul V. Pârvan, 300223 Timişoara, Romania
2Math Department, The “Politehnica” University of Timişoara, Piaţa Victoriei nr. 2, 300006 Timişoara, Romania

Received 21 January 2010; Accepted 29 June 2010

Academic Editor: Marcelo Messias

Copyright © 2011 Gheorghe Ivan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The main purpose of this paper is to study the metriplectic system associated to 3-dimensional Volterra model. For this system we investigate the stability problem and numerical integration via Kahan's integrator. Finally, the synchronization problem for two coupled metriplectic Volterra systems is discussed.