Global projective lag synchronization of fractional order memristor based BAM neural networks with mixed time varying delays

This paper addresses Master–Slave synchronization for some memristor‐based fractional‐order BAM neural networks (MFBNNs) with mixed time varying delays and switching jumps mismatch. Firstly, considering the inherent characteristic of FMNNs, a new type of fractional‐order differential inequality is proposed. Secondly, an adaptive switching control scheme is designed to realize the global projective lag synchronization goal of MFBNNs in the sense of Riemann‐Liouville derivative. Then, based on a suitable Lyapunov method, under the framework of set‐valued map, differential inclusions theory, fractional Barbalat's lemma and proposed control scheme, some new projective lag synchronization criteria for such MFBNNs are obtained. Finally, some numerical examples are presented to illustrate the effectiveness of the proposed theoretical analysis.

[1]  Yang Cao,et al.  Bifurcations in an Internet congestion control system with distributed delay , 2019, Appl. Math. Comput..

[2]  Jinde Cao,et al.  Pinning Synchronization of Nonlinear Coupled Lur’e Networks Under Hybrid Impulses , 2019, IEEE Transactions on Circuits and Systems II: Express Briefs.

[3]  Jinde Cao,et al.  Stability and Hopf bifurcation of controlled complex networks model with two delays , 2019, Appl. Math. Comput..

[4]  Jinde Cao,et al.  Stabilization of Boolean Control Networks Under Aperiodic Sampled-Data Control , 2018, SIAM J. Control. Optim..

[5]  R. Sarpong,et al.  Bio-inspired synthesis of xishacorenes A, B, and C, and a new congener from fuscol† †Electronic supplementary information (ESI) available. See DOI: 10.1039/c9sc02572c , 2019, Chemical science.

[6]  Jinde Cao,et al.  Robust generalized Mittag-Leffler synchronization of fractional order neural networks with discontinuous activation and impulses , 2018, Neural Networks.

[7]  Jinde Cao,et al.  Exponential stability of complex-valued memristor-based neural networks with time-varying delays , 2017, Appl. Math. Comput..

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

[9]  Lingzhong Zhang,et al.  Projective synchronization of fractional-order memristive neural networks with switching jumps mismatch ☆ , 2017 .

[10]  Jinde Cao,et al.  An Impulsive Delay Inequality Involving Unbounded Time-Varying Delay and Applications , 2017, IEEE Transactions on Automatic Control.

[11]  Jinde Cao,et al.  Fixed-time synchronization of delayed memristor-based recurrent neural networks , 2017, Science China Information Sciences.

[12]  Jinde Cao,et al.  Hybrid control on bifurcation for a delayed fractional gene regulatory network , 2016 .

[13]  Jinde Cao,et al.  Lag Synchronization of Memristor-Based Coupled Neural Networks via $\omega $ -Measure , 2016, IEEE Transactions on Neural Networks and Learning Systems.

[14]  Zhigang Zeng,et al.  Global Mittag-Leffler stabilization of fractional-order bidirectional associative memory neural networks , 2016, Neurocomputing.

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

[16]  Quan Yin,et al.  Adaptive Synchronization of Memristor-Based Neural Networks with Time-Varying Delays , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[17]  Jinde Cao,et al.  Mittag-Leffler stability and generalized Mittag-Leffler stability of fractional-order gene regulatory networks , 2015, Neurocomputing.

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

[19]  Jinde Cao,et al.  Pth Moment Exponential Stochastic Synchronization of Coupled Memristor-based Neural Networks with Mixed Delays via Delayed Impulsive Control , 2015, Neural Networks.

[20]  Fei Wang,et al.  Asymptotic stability of delayed fractional-order neural networks with impulsive effects , 2015, Neurocomputing.

[21]  Jinde Cao,et al.  Projective synchronization of fractional-order memristor-based neural networks , 2015, Neural Networks.

[22]  T. Kaczorek,et al.  Fractional Differential Equations , 2015 .

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

[24]  Jinde Cao,et al.  Matrix measure strategies for stability and synchronization of inertial BAM neural network with time delays , 2014, Neural Networks.

[25]  Jinde Cao,et al.  Hybrid control of Hopf bifurcation in complex networks with delays , 2014, Neurocomputing.

[26]  Haijun Jiang,et al.  Projective synchronization for fractional neural networks , 2014, Neural Networks.

[27]  Jinde Cao,et al.  Exponential synchronization of memristive Cohen–Grossberg neural networks with mixed delays , 2014, Cognitive Neurodynamics.

[28]  Zhengwen Tu,et al.  Global dissipativity of a class of BAM neural networks with time-varying and unbound delays , 2013, Commun. Nonlinear Sci. Numer. Simul..

[29]  Zhigang Zeng,et al.  Anti-synchronization control of a class of memristive recurrent neural networks , 2013, Commun. Nonlinear Sci. Numer. Simul..

[30]  W. Marsden.  I and J , 2012 .

[31]  K. Diethelm.  The Analysis of Fractional Differential Equations: An Application-Oriented Exposition Using Differential Operators of Caputo Type , 2010 .

[32]  Johnny Henderson,et al.  Fractional functional differential inclusions with finite delay , 2009 .

[33]  J. Tour,et al.  Electronics: The fourth element , 2008, Nature.

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

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

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

[37]  B Kosko,et al.  Adaptive bidirectional associative memories. , 1987, Applied optics.

[38]  J J Hopfield,et al.  Neural computation by concentrating information in time. , 1987, Proceedings of the National Academy of Sciences of the United States of America.

[39]  Jean-Pierre Aubin,et al.  Differential Inclusions - Set-Valued Maps and Viability Theory , 1984, Grundlehren der mathematischen Wissenschaften.

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