分数阶基因调控网络的拉格朗日稳定性

Lagrange Stability Analysis of Fractional-Order Gene Regulatory Networks

研究了一类分数阶基因调控网络的拉格朗日稳定性问题。首先,将分数阶微分算子引入到传统的整数阶基因调控网络中,建立了新型的分数阶基因调控网络,不仅可以有效地描述系统的记忆遗传特征,还可以真实地反映系统的本质特性;其次,利用拉普拉斯变换方法,卷积公式和Mittag-Leffler函数的性质,得到了此类系统拉格朗日稳定性的充分判据。另外,所得的判据还涵盖了相关整数阶基因调控网络的结果。最后,通过一个仿真实例,验证了该系统拉格朗日稳定性判据的有效性和合理性。

The Lagrange stability for a class of fractional-order gene regulatory networks(FGRN)was investigated.Firstly,a new FGRN was built by introducing fractional-order differential operator into traditional integer-order model,which effectively described memory properties of system and accurately depicted the real characteristics of the system.Then,we obtained some sufficient criteria on Lagrange stability of FGRN by using Laplace transform method,convolution formula and properties of Mittag-Leffler function.It was noted that our results were still hold for integer-order gene regulatory networks.Finally,we verified the validity and rationality of the Lagrange stability of FGRN using an example of simulation.