Stability and Synchronization Control of Fractional-Order Gene Regulatory Network System with Delay
Feng Liu*,†, Zhe Zhang*, Xinmei Wang*, and Fenglan Sun**
*School of Automation, China University of Geosciences
Wuhan 430074, China
**Research Center of System Theory and Application, Chongqing University of Posts and Telecommunications
Chongqing, 400065, China
-  C. Luo and X. Wang, “Chaos in the fractional-order complex Lorenz system and its synchronization,” Nonlinear Dyn, Vol.71, pp. 241-257, 2013.
-  D. Chen, R. Zhang, X. Liu, and X. Ma, “Fractional order Lyapunov stability theorem and its applications in synchronization of complex dynamical networks,” Commun. Nonlear SCI, Vol.9, pp. 4105-4121, 2014.
-  L. Chen, R. Wu, J. Cao, and J. Liu, “Stability and synchronization of memristor-based fractional-order delayed neural networks,” Neural Networks, Vol.71, pp. 37-44, 2015.
-  J. Sun, Q. Han, and X. Jiang, “Impulsive control of time-delay systems using delayed impulse and its application to impulsive master-slave synchronization,” Physics Letters A, Vol.372, pp. 6375-6380, 2008.
-  C. Li, X. Liao, and X. Yang, “Impulsive stabilization and synchronization of a class of chaotic delay systems,” Chaos, Vol.15, 043103, 2005.
-  Y. Wang, W. Yang, J. Xiao, and Z. Zeng, “Impulsive Multi-Synchronization of Coupled Multistable Neural Networks with Time-Varying Delay,” IEEE T NEUR NET LEAR, DOI: 10.1109/TNNLS.2016,2544788, 2016.
-  Y. Li, Y. Chen, and I. Podlubny, “Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag-Leffler stability,” Comp. & Math. Applic, Vol.59, pp. 1810-1821, 2010.
-  X. J. Wen, Z. M. Wu, and J. G. Lu, “Stability analysis of a class of nonlinear fractional-order systems,” IEEE Trans. Circuits Syst. II, Vol.55, pp. 1178-1182, 2008.
-  C. Corduneanu, “Principles of Differential and Integral Equations,” Ams Chelsea Publishing, Boston, 1971.
This article is published under a Creative Commons Attribution-NoDerivatives 4.0 Internationa License.