Finite-Time Projective Synchronization of Fractional-Order Memristive Neural Networks with Mixed Time-Varying Delays

This paper is concerned with the finite-time projective synchronization problem of fractional-order memristive neural networks (FMNNs) with mixed time-varying delays. Firstly, under the frame of fractional-order differential inclusion and the set-valued map, several criteria are derived to ensure finite-time projective synchronization of FMNNs. Meanwhile, three properties are established to deal with different forms of the finite-time fractional differential inequation, which greatly extend some results on estimation of settling time of FMNNs. In addition to the traditional Lyapunov function with 1-norm form in Theorem 1, a more general and flexible Lyapunov function based on p-norm is constructed in Theorem 2 to analyze the finite-time projective synchronization problem, and the estimation of settling time has been verified less conservative than previous results. Finally, numerical examples are provided to demonstrate the effectiveness of the derived theoretical results.

[1]  Xiao Peng,et al.  Global synchronization in finite time for fractional-order neural networks with discontinuous activations and time delays , 2017, Neural Networks.

[2]  Guoguang Wen,et al.  Stability analysis of fractional-order Hopfield neural networks with time delays , 2014, Neural Networks.

[3]  Hu Wang,et al.  Projective synchronization for fractional-order memristor-based neural networks with time delays , 2019, Neural Computing and Applications.

[4]  Wong,et al.  Exponential Asymptotics of the Mittag—Leffler Function , 2002 .

[5]  Jinde Cao,et al.  Finite-time stochastic synchronization of complex networks , 2010 .

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

[7]  C. Y. Chee,et al.  Chaos-based M-ary digital communication technique using controlled projective synchronisation , 2006 .

[8]  Jinde Cao,et al.  Synchronization in uncertain fractional-order memristive complex-valued neural networks with multiple time delays , 2019, Neural Networks.

[9]  Shengfu Deng,et al.  Finite-time projective synchronization of fractional-order complex-valued memristor-based neural networks with delay , 2019, Chaos, Solitons & Fractals.

[10]  Yang Tao,et al.  Impulsive stabilization for control and synchronization of chaotic systems: theory and application to secure communication , 1997 .

[11]  Silvano Donati,et al.  Synchronization of chaotic lasers by optical feedback for cryptographic applications , 1997 .

[12]  Ju H. Park,et al.  Novel results on robust finite-time passivity for discrete-time delayed neural networks , 2016, Neurocomputing.

[13]  Jinde Cao,et al.  LMI-based approach to stability analysis for fractional-order neural networks with discrete and distributed delays , 2018, Int. J. Syst. Sci..

[14]  Hao Zhang,et al.  Topology Identification and Module–Phase Synchronization of Neural Network With Time Delay , 2017, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[15]  Jinde Cao,et al.  Lag projective synchronization of fractional-order delayed chaotic systems , 2019, J. Frankl. Inst..

[16]  Jianwei Xia,et al.  Aperiodically Intermittent Control for Quasi-Synchronization of Delayed Memristive Neural Networks: An Interval Matrix and Matrix Measure Combined Method , 2019, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[17]  Lingzhong Zhang,et al.  Synchronization analysis for fractional order memristive Cohen–Grossberg neural networks with state feedback and impulsive control , 2018, Physica A: Statistical Mechanics and its Applications.

[18]  Haipeng Peng,et al.  Finite-time projective synchronization of memristor-based delay fractional-order neural networks , 2017 .

[19]  Rui Xu,et al.  Synchronization of chaotic neural networks with mixed time delays , 2011 .

[20]  Jinde Cao,et al.  Hybrid Control Scheme for Projective Lag Synchronization of Riemann–Liouville Sense Fractional Order Memristive BAM NeuralNetworks with Mixed Delays , 2019, Mathematics.

[21]  Jinde Cao,et al.  Switching event-triggered control for global stabilization of delayed memristive neural networks: An exponential attenuation scheme , 2019, Neural Networks.

[22]  Haijun Jiang,et al.  Finite-time and fixed-time synchronization of discontinuous complex networks: A unified control framework design , 2018, J. Frankl. Inst..

[23]  Zhen Wang,et al.  Aperiodic Sampled-Data Control for Exponential Stabilization of Delayed Neural Networks: A Refined Two-Sided Looped-Functional Approach , 2020, IEEE Transactions on Circuits and Systems II: Express Briefs.

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

[25]  K. Gopalsamy,et al.  Stability in asymmetric Hopfield nets with transmission delays , 1994 .

[26]  S. Bhat,et al.  Continuous finite-time stabilization of the translational and rotational double integrators , 1998, IEEE Trans. Autom. Control..

[27]  Kotaro Hirasawa,et al.  Solving inequality constrained combinatorial optimization problems by the hopfield neural networks , 1992, Neural Networks.

[28]  Yu Wang,et al.  Global projective synchronization in finite time of nonidentical fractional-order neural networks based on sliding mode control strategy , 2017, Neurocomputing.

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

[30]  Jinde Cao,et al.  Active control strategy for synchronization and anti-synchronization of a fractional chaotic financial system , 2017 .

[31]  Jinde Cao,et al.  Stability and pinning synchronization analysis of fractional order delayed Cohen-Grossberg neural networks with discontinuous activations , 2019, Appl. Math. Comput..

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

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

[34]  Haipeng Peng,et al.  Finite-time projective synchronization of memristor-based neural networks with leakage and time-varying delays , 2019, Physica A: Statistical Mechanics and its Applications.

[35]  Meng Yan,et al.  Stability analysis of memristor-based time-delay fractional-order neural networks , 2019, Neurocomputing.

[36]  Kiyotoshi Matsuoka,et al.  A neural net for blind separation of nonstationary signals , 1995, Neural Networks.

[37]  M. Krstić,et al.  Stochastic nonlinear stabilization—I: a backstepping design , 1997 .

[38]  Massimiliano Di Ventra,et al.  Experimental demonstration of associative memory with memristive neural networks , 2009, Neural Networks.

[39]  Jinde Cao,et al.  Quasi-projective and complete synchronization of fractional-order complex-valued neural networks with time delays , 2019, Neural Networks.

[40]  Haijun Jiang,et al.  Quasi-projective synchronization of fractional-order complex-valued recurrent neural networks , 2018, Neural Networks.

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

[42]  Zhigang Zeng,et al.  Lag Synchronization of Switched Neural Networks via Neural Activation Function and Applications in Image Encryption , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[43]  Jinde Cao,et al.  Global Nonfragile Synchronization in Finite Time for Fractional-Order Discontinuous Neural Networks With Nonlinear Growth Activations , 2019, IEEE Transactions on Neural Networks and Learning Systems.