分数阶基因调控网络的拉格朗日稳定性
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摘要
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.
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.
引文
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[17]WANG H X,LIU G D,SUN Y H,et al.Robust stability of stochastic delayed genetic regulatory networks[J].Cognitive Neurodynamics,2009,3(3):271-280.
[2]刘艳.基因调控网络分析和重建[D].南京:南京理工大学,2004.
[3]ZHANG Z,ZHANG J,AI Z.A novel stability criterion of the time-lag fractional-order gene regulatory network system for stability analysis[J].Communications in Nonlinear Science and Numerical Simulation,2019,66(1):96-108.
[4]杨林,贺大林.Cancer Research:通过基因调控网络分析识别结肠癌药物代谢的性别差异[J].现代泌尿外科杂志,2018,23(12):963-976.
[5]代文哲,黄翔,马静,等.三嗪类衍生物的合成及抑菌活性测定[J].武汉工程大学学报,2018,40(6):606-609.
[6]REN F,CAO F,CAO J.Mittag-Leffler stability and generalized Mittag-Leffler stability of fractional-order gene regulatory networks[J].Neurocomputing,2015,160(6):185-190.
[7]ZHANG Y,PU Y,ZHANG H,et al.An extended fractional Kalman filter for inferring gene regulatory networks using time-series data[J].Chemometrics and Intelligent Laboratory Systems,2014,138:57-63.
[8]何基好,丁倩倩,蔡江华.有限理性与拉格朗日微分中值问题解的稳定性[J].高等数学研究,2017,20(4):10-12.
[9]LIAO X X,LUO Q,ZENG Z G,et al.Global exponential stability in Lagrange sense for recurrent neural networks with time delays[J].Nonlinear Analysis:Real World Applications,2008,9(4):1535-1557.
[10]WU A,ZENG Z,FU C,et al.Global exponential stability in Lagrange sense for periodic neural networks with various activation functions[J].Neurocomputing,2011,74(5):831-837.
[11]易书明,蹇继贵.基于忆阻的脉冲BAM神经网络的拉格朗日稳定性[J].三峡大学学报(自然科学版),2016:38(3):98-103.
[12]何基好.拉格朗日微分中值定理中间点集的稳定性[J].贵州大学学报(自然科学版),2016,33(1):13-15.
[13]吴爱龙.基于忆阻的递归神经网络的动力学分析[D].武汉:华中科技大学,2013.
[14]DIETHELM K,FORD N J.Analysis of fractional differential equations[J].Journal of Mathematical Analysis and Applications,2002,265(2):229-248.
[15]陈立平.分数阶非线性系统的稳定性与同步控制[D].重庆:重庆大学,2013.
[16]XU G,BAO H.The Lagrange stability of fractionalOrder gene regulatory networks[C]//2018 Chinese Automation Congress(CAC).Xi'an:IEEE,2018:3422-3427.
[17]WANG H X,LIU G D,SUN Y H,et al.Robust stability of stochastic delayed genetic regulatory networks[J].Cognitive Neurodynamics,2009,3(3):271-280.