Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 673296, 22 pages
Research Article

Limit-Cycle-Preserving Simulation of Gene Regulatory Oscillators

1Department of Applied Mathematics, Nanjing Agricultural University, Nanjing 210095, China
2State Key Laboratory for Novel Software Technology, Nanjing University, Nanjing 210093, China

Received 9 September 2012; Accepted 18 November 2012

Academic Editor: Xiang Ping Yan

Copyright © 2012 Xiong You. 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.


In order to simulate gene regulatory oscillators more effectively, Runge-Kutta (RK) integrators are adapted to the limit-cycle structure of the system. Taking into account the oscillatory feature of the gene regulatory oscillators, phase-fitted and amplification-fitted Runge-Kutta (FRK) methods are designed. New FRK methods with phase-fitted and amplification-fitted updated are also considered. The error coefficients and the error constant for each of new FRK methods are obtained. In the numerical simulation of the two-gene regulatory system, the new methods are shown to be more accurate and more efficient than their prototype RK methods in the long-term integration. It is a new discovery that the best fitting frequency not only depends on the problem to be solved, but also depends on the method.