Global dynamics of equilibrium point for delayed competitive neural networks with different time scales and discontinuous activations

In this paper, we investigate the global dynamics of equilibrium point for delayed competitive neural networks with different time scales and discontinuous activations. Employing the Leray-Schauder alternative theorem in multivalued analysis, linear matrix inequality technique and generalized Lyapunov-like method, we obtain some new sufficient conditions ensuring the existence, uniqueness and global stability and the global convergence in finite time of the equilibrium point, the results of this paper improve and extend previously known results. Finally, two examples and numerical simulations are conducted to validate the theoretical results.

[1]  Huaiqin Wu,et al.  Stability analysis for periodic solution of neural networks with discontinuous neuron activations , 2009 .

[2]  Hongtao Lu,et al.  Global exponential stability of delayed competitive neural networks with different time scales , 2005, Neural Networks.

[3]  Jinde Cao,et al.  On periodic solutions of neural networks via differential inclusions , 2009, Neural Networks.

[4]  Duccio Papini,et al.  Global exponential stability and global convergence in finite time of delayed neural networks with infinite gain , 2005, IEEE Transactions on Neural Networks.

[5]  BART KOSKO,et al.  Bidirectional associative memories , 1988, IEEE Trans. Syst. Man Cybern..

[6]  Sitian Qin,et al.  Dynamical behavior of a class of nonsmooth gradient-like systems , 2010, Neurocomputing.

[7]  Shengyuan Xu,et al.  New results on global exponential stability of recurrent neural networks with time-varying delays , 2006 .

[8]  Anke Meyer-Bäse,et al.  Local exponential stability of competitive neural networks with different time scales , 2004, Eng. Appl. Artif. Intell..

[9]  Peng Wang,et al.  Global exponential stability of almost periodic solution of delayed neural networks with discontinuous activations , 2013, Inf. Sci..

[10]  Danilo P. Mandic,et al.  A complex-valued nonlinear neural adaptive filter with a gradient adaptive amplitude of the activation function , 2003, Neural Networks.

[11]  Xue-Zhong He,et al.  Delay-independent stability in bidirectional associative memory networks , 1994, IEEE Trans. Neural Networks.

[12]  Zhidong Teng,et al.  Existence and global exponential stability of equilibrium of competitive neural networks with different time scales and multiple delays , 2010, J. Frankl. Inst..

[13]  Anke Meyer-Bäse,et al.  Global exponential stability of competitive neural networks with different time scales , 2003, IEEE Trans. Neural Networks.

[14]  Tianping Chen,et al.  Almost Periodic Dynamics of a Class of Delayed Neural Networks with Discontinuous Activations , 2008, Neural Computation.

[15]  Xuyang Lou,et al.  Synchronization of competitive neural networks with different time scales , 2007 .

[16]  Tianping Chen,et al.  Global exponential stability of almost periodic solution for a large class of delayed dynamical systems , 2005 .

[17]  Jinde Cao,et al.  Existence and global stability of equilibrium point for delayed competitive neural networks with discontinuous activation functions , 2012, Int. J. Syst. Sci..

[18]  Huaguang Zhang,et al.  Dynamical stability analysis of multiple equilibrium points in time-varying delayed recurrent neural networks with discontinuous activation functions , 2012, Neurocomputing.

[19]  Zhigang Zeng,et al.  Analysis and design of associative memories based on recurrent neural network with discontinuous activation functions , 2012, Neurocomputing.

[20]  M. Forti,et al.  Global convergence of neural networks with discontinuous neuron activations , 2003 .

[21]  Duccio Papini,et al.  Global exponential stability of the periodic solution of a delayed neural network with discontinuous activations , 2005 .

[22]  Anke Meyer-Bäse,et al.  Stochastic stability analysis of competitive neural networks with different time-scales , 2013, Neurocomputing.

[23]  Qiankun Song,et al.  Exponential stability of recurrent neural networks with both time-varying delays and general activation functions via LMI approach , 2008, Neurocomputing.

[24]  Tianping Chen,et al.  Dynamical Behaviors of Delayed Neural Network Systems with Discontinuous Activation Functions , 2006, Neural Computation.

[25]  Qintao Gan,et al.  Adaptive synchronization for stochastic competitive neural networks with mixed time-varying delays , 2012 .

[26]  Tianping Chen,et al.  Dynamical Behaviors of Delayed Neural Network Systems with Discontinuous Activation Functions , 2006 .

[27]  Jinde Cao,et al.  Multistability of competitive neural networks with time-varying and distributed delays , 2009 .

[28]  Quan Yin,et al.  Global exponential periodicity and stability of a class of memristor-based recurrent neural networks with multiple delays , 2013, Inf. Sci..

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

[30]  Leon O. Chua,et al.  Cellular neural networks with non-linear and delay-type template elements and non-uniform grids , 1992, Int. J. Circuit Theory Appl..

[31]  Wenlian Lu,et al.  Global almost sure self-synchronization of Hopfield neural networks with randomly switching connections , 2011, Neural Networks.

[32]  J. Cao,et al.  Exponential stability of competitive neural networks with time-varying and distributed delays , 2008 .

[33]  Aleksej F. Filippov,et al.  Differential Equations with Discontinuous Righthand Sides , 1988, Mathematics and Its Applications.

[34]  Shouchuan Hu.  Differential equations with discontinuous right-hand sides☆ , 1991 .

[35]  R. Westervelt,et al.  Stability of analog neural networks with delay. , 1989, Physical review. A, General physics.

[36]  Hongtao Lu,et al.  Global Exponential Stability of Multitime Scale Competitive Neural Networks With Nonsmooth Functions , 2006, IEEE Transactions on Neural Networks.

[37]  Xiangnan Zhou,et al.  Existence and global asymptotic stability of periodic solutions for Hopfield neural networks with discontinuous activations , 2009 .

[38]  Amir F. Atiya,et al.  How delays affect neural dynamics and learning , 1994, IEEE Trans. Neural Networks.

[39]  Jigen Peng,et al.  Exponential stability of a class of generalized neural networks with time-varying delays , 2006, Neurocomputing.

[40]  Sitian Qin,et al.  Global Exponential Stability and Global Convergence in Finite Time of Neural Networks with Discontinuous Activations , 2009, Neural Processing Letters.

[41]  YANGJin-xiang,et al.  Stability for Cellular Neural Networks with Delay , 2005 .

[42]  Anke Meyer-Bäse,et al.  Singular Perturbation Analysis of Competitive Neural Networks with Different Time Scales , 1996, Neural Computation.

[43]  Jiafu Wang,et al.  Almost periodicity for a class of delayed Cohen–Grossberg neural networks with discontinuous activations , 2012 .

[44]  T. Mexia,et al.  Author ' s personal copy , 2009 .

[45]  Sabri Arik,et al.  Global asymptotic stability analysis of bidirectional associative memory neural networks with time delays , 2005, IEEE Transactions on Neural Networks.

[46]  Xinzhi Liu,et al.  Global convergence of neural networks with mixed time-varying delays and discontinuous neuron activations , 2012, Inf. Sci..