Global exponential stability of a class of memristive neural networks with time-varying delays

This paper studies the uniqueness and global exponential stability of the equilibrium point for memristor-based recurrent neural networks with time-varying delays. By employing Lyapunov functional and theory of differential equations with discontinuous right-hand side, we establish several sufficient conditions for exponential stability of the equilibrium point. In comparison with the existing results, the proposed stability conditions are milder and more general, and can be applied to the memristor-based neural networks model whose connection weight changes continuously. Numerical examples are also presented to show the effectiveness of the theoretical results.

[1]  Leon O. Chua,et al.  Memristor Cellular Automata and Memristor Discrete-Time Cellular Neural Networks , 2009, Int. J. Bifurc. Chaos.

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

[3]  Zhigang Zeng,et al.  Exponential synchronization of memristor-based recurrent neural networks with time delays , 2011, Neurocomputing.

[4]  C. Leung,et al.  Hopf bifurcation and chaos in a single delayed neuron equation with non-monotonic activation function , 2001 .

[5]  Jun Wang,et al.  Global uniform asymptotic stability of memristor-based recurrent neural networks with time delays , 2010, The 2010 International Joint Conference on Neural Networks (IJCNN).

[6]  Xiaofeng Liao,et al.  Robust stability for interval Hopfield neural networks with time delay , 1998, IEEE Trans. Neural Networks.

[7]  Chuandong Li,et al.  Impulsive effects on stability of high-order BAM neural networks with time delays , 2011, Neurocomputing.

[8]  Z. Zeng,et al.  Adaptive synchronization of memristor-based Chuaʼs circuits , 2012 .

[9]  Zhigang Zeng,et al.  Dynamics Analysis of a Class of Memristor-Based Recurrent Networks with Time-Varying Delays in the Presence of Strong External Stimuli , 2011, Neural Processing Letters.

[10]  Chuandong Li,et al.  DESTABILIZING EFFECTS OF IMPULSE IN DELAYED BAM NEURAL NETWORKS , 2009 .

[11]  Zhaoning Yu,et al.  Nonlinear optical spectroscopy of photonic metamaterials , 2007, 2008 Conference on Lasers and Electro-Optics and 2008 Conference on Quantum Electronics and Laser Science.

[12]  Chuandong Li,et al.  Delay-Dependent and Delay-Independent Stability Criteria for Cellular Neural Networks with Delays , 2006, Int. J. Bifurc. Chaos.

[13]  Zhang Yi,et al.  Selectable and Unselectable Sets of Neurons in Recurrent Neural Networks With Saturated Piecewise Linear Transfer Function , 2011, IEEE Transactions on Neural Networks.

[14]  Leon O. Chua,et al.  Memristor oscillators , 2008, Int. J. Bifurc. Chaos.

[15]  J. Yang,et al.  Memristive switching mechanism for metal/oxide/metal nanodevices. , 2008, Nature nanotechnology.

[16]  Chaojie Li,et al.  Exponential stability of stochastic high-order BAM neural networks with time delays and impulsive effects , 2013, Neural Computing and Applications.

[17]  X. Liao,et al.  Bifurcation analysis on a two-neuron system with distributed delays , 2001 .

[18]  Z. Zeng,et al.  Dynamic behaviors of a class of memristor-based Hopfield networks , 2011 .

[19]  Chuandong Li,et al.  Bogdanov-Takens bifurcation in a single inertial neuron model with delay , 2012, Neurocomputing.

[20]  Guodong Zhang,et al.  Global exponential stability of a class of memristor-based recurrent neural networks with time-varying delays , 2012, Neurocomputing.

[21]  Chuandong Li,et al.  Exponential stability of impulsive high-order Hopfield-type neural networks with delays and reaction–diffusion , 2011, Int. J. Comput. Math..

[22]  Zhigang Zeng,et al.  Exponential stability analysis of memristor-based recurrent neural networks with time-varying delays , 2012, Neurocomputing.

[23]  Xiaofeng Liao,et al.  Global exponential stability for a class of retarded functional differential equations with applications in neural networks , 2004 .

[24]  D. Stewart,et al.  The missing memristor found , 2008, Nature.

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

[26]  L. Chua.  Memristor-The missing circuit element , 1971 .

[27]  Hai Helen Li,et al.  Spintronic Memristor Through Spin-Torque-Induced Magnetization Motion , 2009, IEEE Electron Device Letters.

[28]  Y. Pershin,et al.  Spin Memristive Systems: Spin Memory Effects in Semiconductor Spintronics , 2008, 0806.2151.