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          華中科技大學學報(自然科學版) 2020, Vol. 48 Issue (12): 27-31 DOI10.13245/j.hust.201205

          丁芝俠 , 陳 沖 , 胡 蝶
          武漢工程大學電氣信息學院,湖北 武漢 430205
          摘要 相比于傳統的整數階基因調控網絡,通過引入分數階微分算子構建了一類新型的分數階時滯基因調控網絡,精確地描述了基因mRNA(信使核糖核酸)和蛋白質之間的關系.針對mRNA和蛋白質之間的復雜動態行為,通過利用Caputo分數階微積分的性質和不等式的放縮技巧,結合所構建的向量范數,給出了系統一致穩定性的充分判據;此外,運用Brower不動點定理證明系統平衡點的存在性和唯一性.所得結論可作為已有文獻的一種推廣,便于實際工程應用.最后,通過仿真實例驗證了所得結論的有效性和正確性.
          關鍵詞 基因調控網絡 ;時滯 ;Caputo分數階微積分 ;向量范數 ;一致穩定性 ;Brower不動點定理
          Uniform stability analysis of fractional-order gene regulatory networks with time delay
          DING Zhixia , CHEN Chong , HU Die
          School of Electrical and Information Engineering,Wuhan Institute of Technology,Wuhan 430205,China
          Abstract Compared with the traditional integer-order gene regulatory networks,a new class of fractional-order gene regulatory networks with time delay was put forward by introducing fractional-order differential operators into integer-order model.Fractional-order gene regulatory networks can accurately describe the relationship between gene mRNA (messenger Ribonucleic Acid) and protein.In order to deal with the complex dynamic behavior between mRNA and protein,the properties of Caputo fractional-order calculus, inequality analysis technique and the constructed vector norm were used.Then,some sufficient criteria for the system's uniform stability were given.In addition, based on the Brower fixed point theorem,the existence and uniqueness of equilibrium point of system were proved.The presented results can be used as a generalization of the existing literature,and they are convenient for practical engineering application.Finally,the validity and correctness of the obtained conclusions was verified by simulation example.
          Keywords gene regulatory networks ; time delay ; Caputo fractional-order calculus ; vector norm ; uniform stability ; Brower fixed point theorem

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