Exponential stability of FCNNs with time-varying leakage delays and reaction-diffusion terms

Abstract In this paper, we investigate the global exponential stability of fuzzy cellular neural networks with time-varying delays in the leakage terms and reaction–diffusion terms. By constructing a novel Lyapunov functional and applying inequality technique, we obtain some new sufficient conditions for the existence, uniqueness and global exponential stability of the equilibrium solution. Moreover, an numerical example is provided to demonstrate the feasibility of our method.

[1]  Hong Zhang,et al.  Existence and exponential stability of anti-periodic solutions for HCNNs with time-varying leakage delays , 2013, Advances in Difference Equations.

[2]  Lihong Huang,et al.  Periodicity and dissipativity for memristor-based mixed time-varying delayed neural networks via differential inclusions , 2014, Neural Networks.

[3]  Jinde Cao,et al.  Global exponential stability and existence of periodic solutions in BAM networks with delays and reaction-diffusion terms , 2005 .

[4]  Lian Duan,et al.  Existence and stability of periodic solution for mixed time-varying delayed neural networks with discontinuous activations , 2014, Neurocomputing.

[5]  Jinde Cao,et al.  Almost periodic solution of shunting inhibitory cellular neural networks with time-varying delay , 2003 .

[6]  Wentao Wang,et al.  Anti-periodic solutions for shunting inhibitory cellular neural networks with time-varying delays in leakage terms , 2013, Neurocomputing.

[7]  Pagavathigounder Balasubramaniam,et al.  Leakage Delays in T–S Fuzzy Cellular Neural Networks , 2011, Neural Processing Letters.

[8]  Pagavathigounder Balasubramaniam,et al.  Asymptotic stability of BAM neural networks of neutral-type with impulsive effects and time delay in the leakage term , 2011, Int. J. Comput. Math..

[9]  Ju H. Park,et al.  Synchronization criteria for coupled stochastic neural networks with time-varying delays and leakage delay , 2012, J. Frankl. Inst..

[10]  Hanlin He,et al.  Guaranteed Cost Synchronization of Chaotic Cellular Neural Networks with Time-Varying Delay , 2012, Neural Computation.

[11]  Zhi-Hong Guan,et al.  Chaotification for a class of cellular neural networks with distributed delays , 2011 .

[12]  Zhenyuan Guo,et al.  Stability and almost periodicity for delayed high-order Hopfield neural networks with discontinuous activations , 2014 .

[13]  Jun-Guo Lu,et al.  Global exponential stability of fuzzy cellular neural networks with delays and reaction–diffusion terms , 2008 .

[14]  Ping Liu,et al.  Existence and stability of periodic solutions of delayed cellular neural networks , 2006 .

[15]  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..

[16]  Ailong Wu,et al.  Global exponential stability of non-autonomous FCNNs with Dirichlet boundary conditions and reaction–diffusion terms , 2010 .

[17]  Tianping Chen,et al.  Global exponential stability of delayed Hopfield neural networks , 2001, Neural Networks.

[18]  K. Gopalsamy Leakage delays in BAM , 2007 .

[19]  Leon O. Chua,et al.  Fuzzy cellular neural networks: applications , 1996, 1996 Fourth IEEE International Workshop on Cellular Neural Networks and their Applications Proceedings (CNNA-96).

[20]  Jin Xu,et al.  On global exponential stability of delayed cellular neural networks with time-varying delays , 2005, Appl. Math. Comput..

[21]  Huaguang Zhang,et al.  Novel stability criterions of a new fuzzy cellular neural networks with time-varying delays , 2009, Neurocomputing.

[22]  Lihong Huang,et al.  Global exponential stability of fuzzy BAM neural networks with distributed delays and time-varying delays in the leakage terms , 2012, Neural Computing and Applications.

[23]  Kelin Li,et al.  Stability analysis of impulsive fuzzy cellular neural networks with distributed delays and reaction-diffusion terms , 2009 .

[24]  Qintao Gan,et al.  Stability Analysis of Stochastic Fuzzy Cellular Neural Networks With Time-Varying Delays and Reaction-Diffusion Terms , 2010, Neural Processing Letters.

[25]  Haijun Jiang,et al.  Global exponential synchronization of fuzzy cellular neural networks with delays and reaction-diffusion terms , 2011, Neurocomputing.

[26]  Leon O. Chua,et al.  Fuzzy cellular neural networks: theory , 1996, 1996 Fourth IEEE International Workshop on Cellular Neural Networks and their Applications Proceedings (CNNA-96).

[27]  Lian Duan,et al.  Global dissipativity of mixed time-varying delayed neural networks with discontinuous activations , 2014, Commun. Nonlinear Sci. Numer. Simul..

[28]  Jinde Cao,et al.  Exponential stability of discrete-time recurrent neural networks with time-varying delays in the leakage terms and linear fractional uncertainties , 2014, IMA J. Math. Control. Inf..

[29]  Junguo Lu Global exponential stability and periodicity of reaction–diffusion delayed recurrent neural networks with Dirichlet boundary conditions , 2008 .

[30]  Qintao Gan,et al.  Global exponential synchronization of generalized stochastic neural networks with mixed time-varying delays and reaction-diffusion terms , 2012, Neurocomputing.

[31]  Hongbin Zhang,et al.  Global exponential stability of impulsive fuzzy Cohen-Grossberg neural networks with mixed delays and reaction-diffusion terms , 2012, Neurocomputing.

[32]  Pagavathigounder Balasubramaniam,et al.  Global robust asymptotic stability analysis of uncertain switched Hopfield neural networks with time delay in the leakage term , 2011, Neural Computing and Applications.

[33]  Bingwen Liu Global exponential stability for BAM neural networks with time-varying delays in the leakage terms☆ , 2013 .

[34]  Pagavathigounder Balasubramaniam,et al.  Robust stability of uncertain fuzzy cellular neural networks with time-varying delays and reaction diffusion terms , 2010, Neurocomputing.