Some new results on periodic solution of Cohen-Grossberg neural network with impulses

In this paper, the periodic solution of Cohen-Grossberg neural network with impulses is studied. Some new sufficient criteria are established to test the existence, exponential stability and stabilization of periodic solution. The results obtained depend mainly on the mean value of the integral of continuous periodic coefficients and the sum of impulsive jumps, and improve some previous related works. Three examples with numerical simulations are given to demonstrate the efficiency of proposed methods.

[1]  Zhanji Gui,et al.  Periodic solutions of nonautonomous cellular neural networks with impulses and delays , 2009 .

[2]  Q. Song,et al.  Global exponential stability of impulsive Cohen-Grossberg neural network with time-varying delays , 2008 .

[3]  Peng Shi,et al.  Control of Nonlinear Networked Systems With Packet Dropouts: Interval Type-2 Fuzzy Model-Based Approach , 2015, IEEE Transactions on Cybernetics.

[4]  Ivanka M. Stamova,et al.  Global exponential stability for impulsive cellular neural networks with time-varying delays , 2008 .

[5]  Jinde Cao,et al.  Stability and periodicity in delayed cellular neural networks with impulsive effects , 2007 .

[6]  Rajcho Ilarionov,et al.  On global exponential stability for impulsive cellular neural networks with time-varying delays , 2010, Comput. Math. Appl..

[7]  R. Jackson.  Inequalities , 2007, Algebra for Parents.

[8]  Bing Li,et al.  Existence and exponential stability of periodic solution for impulsive Cohen-Grossberg neural networks with time-varying delays , 2012, Appl. Math. Comput..

[9]  S. Mohamad,et al.  Exponential stability in Hopfield-type neural networks with impulses , 2007 .

[10]  Yingnan Pan,et al.  Filter Design for Interval Type-2 Fuzzy Systems With D Stability Constraints Under a Unified Frame , 2015, IEEE Transactions on Fuzzy Systems.

[11]  Martin Bohner,et al.  Impulsive differential equations: Periodic solutions and applications , 2015, Autom..

[12]  Benedetta Lisena,et al.  Exponential stability of Hopfield neural networks with impulses , 2011 .

[13]  Yuanfu Shao,et al.  Exponential stability of periodic neural networks with impulsive effects and time-varying delays , 2011, Appl. Math. Comput..

[14]  Daoyi Xu,et al.  Impulsive effects on stability of Cohen-Grossberg neural networks with variable delays , 2006, Appl. Math. Comput..

[15]  Ivanka M. Stamova,et al.  Asymptotic stability of an N-dimensional impulsive competitive system , 2007 .

[16]  Enrique Romero-Cadaval,et al.  Grid-Connected Photovoltaic Generation Plants: Components and Operation , 2013, IEEE Industrial Electronics Magazine.

[17]  K. Gopalsamy.  Stability and Oscillations in Delay Differential Equations of Population Dynamics , 1992 .

[18]  Jinde Cao,et al.  Exponential input-to-state stability of stochastic Cohen–Grossberg neural networks with mixed delays , 2014, Nonlinear Dynamics.

[19]  Jinde Cao,et al.  Mean-square exponential input-to-state stability of stochastic delayed neural networks , 2014, Neurocomputing.

[21]  Hongyong Zhao,et al.  Existence and stability of almost periodic solution for Cohen–Grossberg neural networks with variable coefficients☆ , 2008 .

[22]  Benedetta Lisena.  Dynamical behavior of impulsive and periodic CohenGrossberg neural networks , 2011 .

[23]  Ligang Wu,et al.  State and Output Feedback Control of Interval Type-2 Fuzzy Systems With Mismatched Membership Functions , 2015, IEEE Transactions on Fuzzy Systems.

[24]  Jinde Cao,et al.  Stability of Markovian jump neural networks with impulse control and time varying delays , 2012 .

[25]  Xiaodi Li,et al.  Existence and global exponential stability of periodic solution for impulsive Cohen-Grossberg-type BAM neural networks with continuously distributed delays , 2009, Appl. Math. Comput..

[26]  H. Lam.  State and Output Feedback Control of A Class of Fuzzy Systems with Mismatched Membership Functions , 2014 .

[27]  Jinde Cao,et al.  On the Exponential Stability and Periodic Solutions of Delayed Cellular Neural Networks , 2000 .

[28]  Xinsong Yang.  Existence and global exponential stability of periodic solution for Cohen-Grossberg shunting inhibitory cellular neural networks with delays and impulses , 2009, Neurocomputing.

[29]  Tianping Chen,et al.  Delay-independent stability analysis of Cohen-Grossberg neural networks , 2003 .

[30]  Chuanzhi Bai,et al.  Global exponential stability and existence of periodic solution of Cohen–Grossberg type neural networks with delays and impulses , 2008 .

[31]  R. Rakkiyappan,et al.  Stochastic stability of Markovian jump BAM neural networks with leakage delays and impulse control , 2014, Neurocomputing.

[32]  Ligang Wu,et al.  Filtering of Interval Type-2 Fuzzy Systems With Intermittent Measurements , 2016, IEEE Transactions on Cybernetics.

[33]  Hak-Keung Lam,et al.  Model reduction for interval type-2 Takagi-Sugeno fuzzy systems , 2015, Autom..

[34]  Weirui Zhao.  Dynamics of Cohen–Grossberg neural network with variable coefficients and time-varying delays , 2008 .

[35]  Jianbin Qiu,et al.  A Combined Adaptive Neural Network and Nonlinear Model Predictive Control for Multirate Networked Industrial Process Control , 2016, IEEE Transactions on Neural Networks and Learning Systems.

[36]  K. Gopalsamy,et al.  Stability of artificial neural networks with impulses , 2004, Appl. Math. Comput..

[37]  Huiyan Kang,et al.  Global exponential stability of periodic solutions for impulsive Cohen–Grossberg neural networks with delays , 2015 .

[38]  Daoyi Xu,et al.  Impulsive delay differential inequality and stability of neural networks , 2005 .

[39]  Leopoldo García Franquelo,et al.  Selective Harmonic Mitigation Technique for Cascaded H-Bridge Converters With Nonequal DC Link Voltages , 2013, IEEE Transactions on Industrial Electronics.

[40]  Shair Ahmad,et al.  Extinction in nonautonomous T-periodic competitive Lotka-Volterra system , 1998 .