New results on the general decay synchronization of delayed neural networks with general activation functions

Abstract This paper investigates the general decay synchronization (GDS) of a type of neural networks (NNs) with general neuron activation functions and varying-time delays. By introducing suitable Lyapunov functional and employing useful inequality techniques, some simple and useful sufficient conditions ensuring the GDS of considered NNs are established via designing a novel nonlinear feedback controller. In addition, two examples are presented to show the effectiveness of the established theoretical results. The polynomial synchronization, asymptotical synchronization, and exponential synchronization can be seen the special cases of the GDS.

[1]  Sabri Arik,et al.  A new condition for robust stability of uncertain neural networks with time delays , 2014, Neurocomputing.

[2]  Martin Hasler,et al.  Recursive neural networks for associative memory , 1990, Wiley-interscience series in systems and optimization.

[3]  Zhidong Teng,et al.  Finite-time synchronization for fuzzy cellular neural networks with time-varying delays , 2016, Fuzzy Sets Syst..

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

[5]  R. Konnur.  Synchronization-based approach for estimating all model parameters of chaotic systems. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  K. Gopalsamy,et al.  Stability in asymmetric Hopfield nets with transmission delays , 1994 .

[7]  M. Zochowski.  Intermittent dynamical control , 2000 .

[8]  Manfeng Hu,et al.  Adaptive feedback controller for projective synchronization , 2008 .

[9]  Vedat Tavsanoglu,et al.  Global asymptotic stability analysis of bidirectional associative memory neural networks with constant time delays , 2005, Neurocomputing.

[10]  Jinde Cao,et al.  Asymptotic and robust stability of genetic regulatory networks with time-varying delays , 2008, Neurocomputing.

[11]  M. Feki.  An adaptive chaos synchronization scheme applied to secure communication , 2003 .

[12]  Haijun Jiang,et al.  The existence and stability of the anti-periodic solution for delayed Cohen-Grossberg neural networks with impulsive effects , 2015, Neurocomputing.

[13]  Guodong Zhang,et al.  General decay synchronization stability for a class of delayed chaotic neural networks with discontinuous activations , 2016, Neurocomputing.

[14]  J J Hopfield,et al.  Neural networks and physical systems with emergent collective computational abilities. , 1982, Proceedings of the National Academy of Sciences of the United States of America.

[15]  Tianping Chen,et al.  Global $\mu$ -Stability of Delayed Neural Networks With Unbounded Time-Varying Delays , 2007, IEEE Transactions on Neural Networks.

[16]  Daoyi Xu,et al.  Stability Analysis and Design of Impulsive Control Systems With Time Delay , 2007, IEEE Transactions on Automatic Control.

[17]  Z. Teng,et al.  Function projective synchronization of impulsive neural networks with mixed time-varying delays , 2014 .

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

[19]  Guodong Zhang,et al.  Synchronization of a Class of Switched Neural Networks with Time-Varying Delays via Nonlinear Feedback Control , 2016, IEEE Transactions on Cybernetics.

[20]  Z. Teng,et al.  Fuzzy Impulsive Control and Synchronization of General Chaotic System , 2010 .

[21]  Zhidong Teng,et al.  Lag synchronization for Cohen–Grossberg neural networks with mixed time-delays via periodically intermittent control , 2017, Int. J. Comput. Math..

[22]  G. Rangarajan,et al.  Stability of synchronized chaos in coupled dynamical systems , 2002, nlin/0201037.

[23]  Hieu Trinh,et al.  New generalized Halanay inequalities with applications to stability of nonlinear non-autonomous time-delay systems , 2015 .