Periodicity and dissipativity for memristor-based mixed time-varying delayed neural networks via differential inclusions

In this paper, we investigate a class of memristor-based neural networks with general mixed delays involving both time-varying delays and distributed delays. By using the Mawhin-like coincidence theorem, together with the differential inclusion theory, M-matrix properties and differential inequality techniques, some novel criteria are established for ensuring the periodicity and dissipativity for the addressed neural networks. Finally, two numerical examples with simulations are presented to demonstrate the effectiveness of the theoretical results.

[1]  Tamás Roska,et al.  Image compression by cellular neural networks , 1998 .

[2]  Sanbo Ding,et al.  Complete Periodic Synchronization of Memristor-Based Neural Networks with Time-Varying Delays , 2013 .

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

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

[5]  Jun Wang,et al.  Global asymptotic stability and global exponential stability of continuous-time recurrent neural networks , 2002, IEEE Trans. Autom. Control..

[6]  Jun Wang,et al.  Almost Sure Exponential Stability of Recurrent Neural Networks With Markovian Switching , 2009, IEEE Transactions on Neural Networks.

[7]  Jun Wang,et al.  Attractivity Analysis of Memristor-Based Cellular Neural Networks With Time-Varying Delays , 2014, IEEE Transactions on Neural Networks and Learning Systems.

[8]  Zhigang Zeng,et al.  Dynamic behaviors of memristor-based recurrent neural networks with time-varying delays , 2012, Neural Networks.

[9]  Q. Song,et al.  Global dissipativity of neural networks with both variable and unbounded delays , 2005 .

[10]  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).

[11]  J. Suehle,et al.  A Flexible Solution-Processed Memristor , 2009, IEEE Electron Device Letters.

[12]  Guodong Zhang,et al.  Global anti-synchronization of a class of chaotic memristive neural networks with time-varying delays , 2013, Neural Networks.

[13]  Leon O. Chua,et al.  Circuit Elements With Memory: Memristors, Memcapacitors, and Meminductors , 2009, Proceedings of the IEEE.

[14]  Jinde Cao,et al.  Robust State Estimation for Neural Networks With Discontinuous Activations , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[15]  Huaiqin Wu,et al.  Almost Periodic Solution for Memristive Neural Networks with Time-Varying Delays , 2013, J. Appl. Math..

[16]  K. D. Cantley,et al.  Hebbian Learning in Spiking Neural Networks With Nanocrystalline Silicon TFTs and Memristive Synapses , 2011, IEEE Transactions on Nanotechnology.

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

[18]  Li Yong,et al.  Periodic solutions of differential inclusions , 1995 .

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

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

[21]  Zhigang Zeng,et al.  Passivity analysis of memristor-based recurrent neural networks with time-varying delays , 2013, J. Frankl. Inst..

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

[23]  Zhigang Zeng,et al.  Synchronization control of a class of memristor-based recurrent neural networks , 2012, Inf. Sci..

[24]  Massimiliano Di Ventra,et al.  Memristive model of amoeba learning. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[26]  Yu. S. Ledyaev,et al.  Nonsmooth analysis and control theory , 1998 .

[27]  Jinde Cao,et al.  Global Asymptotical Stability of Recurrent Neural Networks With Multiple Discrete Delays and Distributed Delays , 2006, IEEE Transactions on Neural Networks.

[28]  Jun Wang,et al.  Global dissipativity of continuous-time recurrent neural networks with time delay. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[29]  Ronald J. Williams,et al.  A Learning Algorithm for Continually Running Fully Recurrent Neural Networks , 1989, Neural Computation.

[30]  Richard A. Chapman,et al.  Neural Learning Circuits Utilizing Nano-Crystalline Silicon Transistors and Memristors , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[31]  Lihong Huang,et al.  Global convergence of periodic solution of neural networks with discontinuous activation functions , 2009 .

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

[33]  Leon O. Chua,et al.  Simplest Chaotic Circuit , 2010, Int. J. Bifurc. Chaos.

[34]  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.

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

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

[37]  M. Forti,et al.  Global Convergence of Neural Networks With , 2003 .

[38]  S. Benderli,et al.  On SPICE macromodelling of TiO 2 memristors , 2009 .

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

[40]  Jun Wang,et al.  Global exponential dissipativity and stabilization of memristor-based recurrent neural networks with time-varying delays , 2013, Neural Networks.

[41]  B. Duenweg,et al.  散逸粒子動力学:平衡および非平衡分子動力学シミュレーションのための有用なサーモスタット(原標題は英語) , 2003 .