Global $\mu$ -Synchronization of Linearly Coupled Unbounded Time-Varying Delayed Neural Networks With Unbounded Delayed Coupling

In this brief, we study the global synchronization of linearly coupled neural networks with delayed couplings, where the intrinsic systems are recurrently connected neural networks with unbounded time-varying delays, and the couplings include instant couplings and unbounded delayed couplings. The concept of mu-synchronization is introduced. Some sufficient conditions are derived for the global mu-synchronization for the underlined coupled systems.

[1]  Insley B. Pyne,et al.  Linear programming on an electronic analogue computer , 1956, Transactions of the American Institute of Electrical Engineers, Part I: Communication and Electronics.

[2]  A. Winfree The geometry of biological time , 1991 .

[3]  Leon O. Chua,et al.  Neural networks for nonlinear programming , 1988 .

[4]  Carroll,et al.  Synchronization in chaotic systems. , 1990, Physical review letters.

[5]  Shengwei Zhang,et al.  Lagrange programming neural networks , 1992 .

[6]  Abdesselam Bouzerdoum,et al.  Neural network for quadratic optimization with bound constraints , 1993, IEEE Trans. Neural Networks.

[7]  Carroll,et al.  Synchronous chaos in coupled oscillator systems. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[8]  A. Tesi,et al.  New conditions for global stability of neural networks with application to linear and quadratic programming problems , 1995 .

[9]  L. Chua,et al.  Synchronization in an array of linearly coupled dynamical systems , 1995 .

[10]  Youshen Xia,et al.  A new neural network for solving linear and quadratic programming problems , 1996, IEEE Trans. Neural Networks.

[11]  Kwong-Sak Leung,et al.  A new gradient-based neural network for solving linear and quadratic programming problems , 2001, IEEE Trans. Neural Networks.

[12]  Jürgen Kurths,et al.  Synchronization - A Universal Concept in Nonlinear Sciences , 2001, Cambridge Nonlinear Science Series.

[13]  S. Strogatz Exploring complex networks , 2001, Nature.

[14]  Xiao Fan Wang,et al.  Synchronization in scale-free dynamical networks: robustness and fragility , 2001, cond-mat/0105014.

[15]  Jürgen Kurths,et al.  Synchronization: Phase locking and frequency entrainment , 2001 .

[16]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[17]  N. Buric,et al.  Synchronization of hyperchaotic systems with delayed bidirectional coupling. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  Mingzhou Ding,et al.  Enhancement of neural synchrony by time delay. , 2004, Physical review letters.

[19]  Tianping Chen,et al.  Synchronization of coupled connected neural networks with delays , 2004, IEEE Transactions on Circuits and Systems I: Regular Papers.

[20]  M. Rosenblum,et al.  Delayed feedback control of collective synchrony: an approach to suppression of pathological brain rhythms. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  Chunguang Li,et al.  Synchronization in general complex dynamical networks with coupling delays , 2004 .

[22]  M. Lakshmanan,et al.  Transition from anticipatory to lag synchronization via complete synchronization in time-delay systems. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  Tianping Chen,et al.  Synchronization in general complex delayed dynamical networks , 2006, IEEE Transactions on Circuits and Systems I: Regular Papers.

[24]  Tianping Chen,et al.  New approach to synchronization analysis of linearly coupled ordinary differential systems , 2006 .

[25]  Elisa Ricci,et al.  Analog neural network for support vector machine learning , 2006, IEEE Transactions on Neural Networks.

[26]  Tianping Chen,et al.  Synchronization analysis of linearly coupled systems described by differential equations with a coupling delay , 2006 .

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

[28]  Wei Wu,et al.  Global Synchronization Criteria of Linearly Coupled Neural Network Systems With Time-Varying Coupling , 2008, IEEE Transactions on Neural Networks.

[29]  G. Lin Nonlinear Programming without Computation , 2022 .