O(t-α)-synchronization and Mittag-Leffler synchronization for the fractional-order memristive neural networks with delays and discontinuous neuron activations

This paper investigates O(t-α)-synchronization and adaptive Mittag-Leffler synchronization for the fractional-order memristive neural networks with delays and discontinuous neuron activations. Firstly, based on the framework of Filippov solution and differential inclusion theory, using a Razumikhin-type method, some sufficient conditions ensuring the global O(t-α)-synchronization of considered networks are established via a linear-type discontinuous control. Next, a new fractional differential inequality is established and two new discontinuous adaptive controller is designed to achieve Mittag-Leffler synchronization between the drive system and the response systems using this inequality. Finally, two numerical simulations are given to show the effectiveness of the theoretical results. Our approach and theoretical results have a leading significance in the design of synchronized fractional-order memristive neural networks circuits involving discontinuous activations and time-varying delays.

[1]  R. Rakkiyappan,et al.  Hybrid projective synchronization of fractional-order memristor-based neural networks with time delays , 2015, Nonlinear Dynamics.

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

[3]  Haijun Jiang,et al.  New results on exponential synchronization of memristor-based neural networks with discontinuous neuron activations , 2016, Neural Networks.

[4]  Ligang Wu,et al.  Receding Horizon Stabilization and Disturbance Attenuation for Neural Networks With Time-Varying Delay , 2015, IEEE Transactions on Cybernetics.

[5]  Jinde Cao,et al.  New synchronization criteria for memristor-based networks: Adaptive control and feedback control schemes , 2015, Neural Networks.

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

[7]  Hamid Reza Karimi,et al.  Stability of Markovian Jump Generalized Neural Networks With Interval Time-Varying Delays , 2017, IEEE Transactions on Neural Networks and Learning Systems.

[8]  Ju H. Park,et al.  Exponential synchronization for fractional-order chaotic systems with mixed uncertainties , 2015, Complex..

[9]  Chuandong Li,et al.  Stability of delayed memristive neural networks with time-varying impulses , 2014, Cognitive Neurodynamics.

[10]  Jinde Cao,et al.  Finite-time synchronization of fractional-order memristor-based neural networks with time delays , 2016, Neural Networks.

[11]  H. Srivastava,et al.  Theory and Applications of Fractional Differential Equations , 2006 .

[12]  R. Rakkiyappan,et al.  Stability analysis of memristor-based complex-valued recurrent neural networks with time delays , 2016, Complex..

[13]  Daniel W. C. Ho,et al.  Synchronization of Delayed Memristive Neural Networks: Robust Analysis Approach , 2016, IEEE Transactions on Cybernetics.

[14]  Jinde Cao,et al.  Adaptive synchronization of fractional-order memristor-based neural networks with time delay , 2015, Nonlinear Dynamics.

[15]  I. Podlubny.  Fractional differential equations , 1998 .

[16]  I. Stamova.  Global Mittag-Leffler stability and synchronization of impulsive fractional-order neural networks with time-varying delays , 2014, Nonlinear Dynamics.

[17]  Jiejie Chen,et al.  Global O(t-α) stability and global asymptotical periodicity for a non-autonomous fractional-order neural networks with time-varying delays , 2016, Neural Networks.

[18]  Lixiang Li,et al.  Synchronization control of memristor-based recurrent neural networks with perturbations , 2014, Neural Networks.

[19]  Ju H. Park,et al.  Reliable mixed passive and ℋ∞ filtering for semi‐Markov jump systems with randomly occurring uncertainties and sensor failures , 2015 .

[20]  Jiejie Chen,et al.  Global asymptotical ω-periodicity of a fractional-order non-autonomous neural networks , 2015, Neural Networks.

[21]  Jinde Cao,et al.  Exponential Synchronization of Memristive Neural Networks With Delays: Interval Matrix Method , 2017, IEEE Transactions on Neural Networks and Learning Systems.

[22]  Jiejie Chen,et al.  Razumikhin-type stability theorems for functional fractional-order differential systems and applications , 2015, Appl. Math. Comput..

[23]  Jinde Cao,et al.  Synchronization of fractional-order complex-valued neural networks with time delay , 2016, Neural Networks.

[24]  Zhongli Wei,et al.  Initial value problems for fractional differential equations involving Riemann–Liouville sequential fractional derivative , 2010 .

[25]  Zhigang Zeng,et al.  Global exponential almost periodicity of a delayed memristor-based neural networks , 2014, Neural Networks.

[26]  Jinde Cao,et al.  Synchronization of memristor-based recurrent neural networks with two delay components based on second-order reciprocally convex approach , 2014, Neural Networks.

[27]  Jun Wang,et al.  Global Exponential Synchronization of Two Memristor-Based Recurrent Neural Networks With Time Delays via Static or Dynamic Coupling , 2015, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

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

[29]  Zhigang Zeng,et al.  Global Mittag-Leffler stability and synchronization of memristor-based fractional-order neural networks , 2014, Neural Networks.

[30]  Zhigang Zeng,et al.  On the periodic dynamics of memristor-based neural networks with time-varying delays , 2014, Inf. Sci..