Finite-time synchronization of fractional-order gene regulatory networks with time delay

As multi-gene networks transmit signals and products by synchronous cooperation, investigating the synchronization of gene regulatory networks may help us to explore the biological rhythm and internal mechanisms at molecular and cellular levels. We aim to induce a type of fractional-order gene regulatory networks to synchronize at finite-time point by designing feedback controls. Firstly, a unique equilibrium point of the network is proved by applying the principle of contraction mapping. Secondly, some sufficient conditions for finite-time synchronization of fractional-order gene regulatory networks with time delay are explored based on two kinds of different control techniques and fractional Lyapunov function approach, and the corresponding setting time is estimated. Finally, some numerical examples are given to demonstrate the effectiveness of the theoretical results.

[1]  Xiaodi Li,et al.  Global exponential stability of a class of impulsive cellular neural networks with supremums , 2014 .

[2]  Kunlun Wang,et al.  Dynamical behaviors of Cohen-Grossberg neural networks with delays and reaction-diffusion terms , 2006, Neurocomputing.

[3]  Jinde Cao,et al.  Mittag-Leffler stability and generalized Mittag-Leffler stability of fractional-order gene regulatory networks , 2015, Neurocomputing.

[4]  Jinde Cao,et al.  Robust generalized Mittag-Leffler synchronization of fractional order neural networks with discontinuous activation and impulses , 2018, Neural Networks.

[5]  Jinde Cao,et al.  Stability and synchronization criteria for fractional order competitive neural networks with time delays: An asymptotic expansion of Mittag Leffler function , 2019, J. Frankl. Inst..

[6]  Hidde de Jong,et al.  Modeling and Simulation of Genetic Regulatory Systems: A Literature Review , 2002, J. Comput. Biol..

[7]  Quanxin Zhu,et al.  Generalized lag-synchronization of chaotic mix-delayed systems with uncertain parameters and unknown perturbations , 2011 .

[8]  Haijun Jiang,et al.  Projective synchronization for fractional neural networks , 2014, Neural Networks.

[9]  Xiaodi Li,et al.  Existence and global stability analysis of equilibrium of fuzzy cellular neural networks with time delay in the leakage term under impulsive perturbations , 2011, J. Frankl. Inst..

[10]  Jinde Cao,et al.  Impulsive discrete-time GRNs with probabilistic time delays, distributed and leakage delays: an asymptotic stability issue , 2019, IMA J. Math. Control. Inf..

[11]  Liping Chen,et al.  Pinning synchronization of fractional-order delayed complex networks with non-delayed and delayed couplings , 2017, Int. J. Control.

[12]  Jinde Cao,et al.  Disparate delays-induced bifurcations in a fractional-order neural network , 2019, J. Frankl. Inst..

[13]  Jinde Cao,et al.  Further synchronization in finite time analysis for time-varying delayed fractional order memristive competitive neural networks with leakage delay , 2018, Neurocomputing.

[14]  Yigang He,et al.  New Result on Finite-Time Stability of Fractional-Order Nonlinear Delayed Systems , 2015 .

[15]  Jinde Cao,et al.  Approximation of state variables for discrete-time stochastic genetic regulatory networks with leakage, distributed, and probabilistic measurement delays: a robust stability problem , 2018, Advances in Difference Equations.

[16]  Lei Shi,et al.  Finite-time synchronization for competitive neural networks with mixed delays and non-identical perturbations , 2016, Neurocomputing.

[17]  Lihong Huang,et al.  Periodic orbit analysis for the delayed Filippov system , 2018, Proceedings of the American Mathematical Society.

[18]  Chuangxia Huang,et al.  Periodicity of non-autonomous inertial neural networks involving proportional delays and non-reduced order method , 2019, International Journal of Biomathematics.

[19]  Feng Liu,et al.  Stability and Synchronization Control of Fractional-Order Gene Regulatory Network System with Delay , 2017, J. Adv. Comput. Intell. Intell. Informatics.

[20]  Tonghua Zhang,et al.  Bifurcation analysis of a mathematical model for genetic regulatory network with time delays , 2015, Appl. Math. Comput..

[21]  Ma Xin,et al.  Modelling gene regulatory network by fractional order differential equations , 2010, 2010 IEEE Fifth International Conference on Bio-Inspired Computing: Theories and Applications (BIC-TA).

[22]  Lihong Huang,et al.  Dynamics of anti-periodic solutions on shunting inhibitory cellular neural networks with multi-proportional delays , 2019, Neurocomputing.

[23]  Jinde Cao,et al.  Hybrid control on bifurcation for a delayed fractional gene regulatory network , 2016 .

[24]  Chuangxia Huang,et al.  On the basins of attraction for a class of delay differential equations with non-monotone bistable nonlinearities , 2014 .

[25]  Jinde Cao,et al.  Robust Synchronization of Fractional-Order Uncertain Chaotic Systems Based on Output Feedback Sliding Mode Control , 2019, Mathematics.

[26]  Rathinasamy Sakthivel,et al.  Asymptotic stability of delayed stochastic genetic regulatory networks with impulses , 2010 .

[27]  Lihong Huang,et al.  The number and stability of limit cycles for planar piecewise linear systems of node–saddle type , 2019, Journal of Mathematical Analysis and Applications.

[28]  Zhigang Zeng,et al.  Global Mittag-Leffler stabilization of fractional-order bidirectional associative memory neural networks , 2016, Neurocomputing.

[29]  Jinde Cao,et al.  Novel bifurcation results for a delayed fractional-order quaternion-valued neural network , 2019, Neural Networks.

[30]  Lihong Huang,et al.  Discontinuity-induced limit cycles in a general planar piecewise linear system of saddle–focus type , 2019, Nonlinear Analysis: Hybrid Systems.

[31]  Zhe Zhang,et al.  Synchronization of fractional-order gene regulatory network with delay , 2017, 2017 36th Chinese Control Conference (CCC).

[32]  Shiqi Zheng,et al.  Analysis and Fractional PD Control Bifurcation of a Fractional-Order Genetic Regulatory Networks with Delays , 2018, 2018 37th Chinese Control Conference (CCC).

[33]  Haijun Hu,et al.  Existence of an extinction wave in the Fisher equation with a shifting habitat , 2017 .

[34]  Jinde Cao,et al.  Stabilization of Switched Stochastic Genetic Regulatory Networks with Leakage and Impulsive Effects , 2018, Neural Processing Letters.