Citation: | ZHANG Weiwei, CHEN Dingyuan, WU Ranchao, CAO Jinde. Modified-Projective-Synchronization of Memristor-Based Fractional-Order Delayed Neural Networks[J]. Applied Mathematics and Mechanics, 2018, 39(2): 239-248. doi: 10.21656/1000-0887.370359 |
[1] |
PODLUBNY I. Fractional Differential Equations [M]. New York: Academic Press, 1999: 105-114.
|
[2] |
BUTZER P L, WESTPHAL U. An Introduction to Fractional Calculus [M]. Singapore: World Scientic, 2000: 22-45.
|
[3] |
MANDELBROT B B. The Fractal Geometry of Nature [M]. New York: Freeman, 1996: 65-69.
|
[4] |
Hilfer R. Applications of Fractional Calculus in Physics [M]. NJ: World Scientic, 2001: 87-92.
|
[5] |
KILBAS A A, SRIVASTAVA H M, TRUJILLO J J. Theory and Application of Fractional Differential Equations [M]. Amsterdam: Elsevier, 2006: 43-48.
|
[6] |
BAO Haibo, CAO Jinde. Projective synchronization of fractional-order memristor-based neural networks[J]. Neural Networks,2015,63(2): 1-9.
|
[7] |
YU Juan, HUA Cheng, JIANG Haijun, et al. Projective synchronization for fractional neural networks[J]. Neural Networks,2014,49(2): 87-95.
|
[8] |
KASLIK E, SIVASUNDARAM S. Nonlinear dynamics and chaos in fractional-order neural networks[J]. Neural Networks,2012,32(3): 245-256.
|
[9] |
CHEN Jiejie, ZENG Zhigang, JIANG Ping. Global Mittag-Leffler stability and synchronization of memristor-based fractional-order neural networks[J]. Neural Networks,2014,51(2): 1-8.
|
[10] |
WU Ailong, WEN Shiping, ZENG Zhigang. Synchronization control of a class of memristor-based recurrent neural networks[J]. Information Sciences,2012,183(1): 106-116.
|
[11] |
LI Ning, CAO Jinde. New synchronization criteria for memristor-based networks: adaptive control and feedback control schemes[J]. Neural Networks,2015,61: 1-9.
|
[12] |
CHAKRABORTY K, CHAKRABORTY M, KAR T K. Bifurcation and control of a bioeconomic model of a prey-predator system with a time delay[J]. Nonlinear Analysis: Hybrid Systems,2011,5(4): 613-625.
|
[13] |
MA Chao, WANG Xingyuan. Impulsive control and synchronization of a new unified hyperchaotic system with varying control gains and impulsive intervals[J]. Nonlinear Dynamics,2012,70(1): 551-558.
|
[14] |
闫欢, 赵振江, 宋乾坤. 具有泄漏时滞的复值神经网络的全局同步性[J]. 应用数学和力学, 2016,37(8): 832-841.(YAN Huan, ZHAO Zhenjiang, SONG Qiankun. Global synchronization of complex-valued neural networks with leakage time delays[J]. Applied Mathematics and Mechanics,2016,37(8): 832-841.(in Chinese))
|
[15] |
ZHAO Hongyong, ZHANG Qi. Global impulsive exponential anti-synchronization of delayed chaotic neural networks[J]. Neurocomputing,2011,74(4): 563-567.
|
[16] |
WANG Ling, ZHAO Hongyong. Synchronized stability in a reaction-diffusion neural network model[J]. Physics Letters A,2014,378(48): 3586-3599.
|
[17] |
WANG Ling, ZHAO Hongyong, CAO Jinde. Synchronized bifurcation and stability in a ring of diffusively coupled neurons with time delay[J]. Neural Networks,2016,75: 32-46.
|
[18] |
PECORA L M, CARROLL T L. Synchronization in chaotic systems[J]. Physical Review Letters,1990,64(8): 821-824.
|
[19] |
RAKKIYAPPAN R, VELMURUGAN G, CAO Jinde. Finite-time stability analysis of fractional-order complex-valued memristor-based neural networks with time delays[J]. Nonlinear Dynamics,2014,78(4): 2823-2832.
|
[20] |
WU Ranchao, LU Yanfen, CHEN Liping. Finite-time stability of fractional delayed neural networks[J]. Neurocomputing,2015,149: 700-707.
|
[21] |
STAMOVA I. Global Mittag-Leffler stability and synchronization of impulsive fractional-order neural networks with time-varying delays[J]. Nonlinear Dynamics,2014,77(4): 1-10.
|
[22] |
CHUA L O. Memristor—the missing circuit element[J]. IEEE Transactions on Circuit Theory,1971,18(5): 507-519.
|
[23] |
STRUKOV D B, SNIDER G S, STEWART D R, et al. The missing memristor found[J]. Nature,2011,453(7191): 80-88.
|
[24] |
TOUR J M, HE Tao. Electronics: the fourth element[J]. Nature,2011,453(7191): 42-43.
|
[25] |
胡进, 宋乾坤. 基于忆阻的时滞神经网络的全局稳定性[J]. 应用数学和力学, 2013,34(7): 724-735.(HU Jin, SONG Qiankun. Global uniform asymptotic stability of memristor-based recurrent neural networks with time delays[J].Applied Mathematics and Mechanics,2013,34(7): 724-735.(in Chinese))
|
[26] |
GUO Zhenyuan, WANG Jun, YAN Zheng. Attractivity analysis of memristor-based cellular neural networks with time-varying delays[J]. IEEE Transactions on Neural Networks and Learning Systems,2014,25(4): 704-717.
|
[27] |
WEN Shiping, BAO Gang, ZENG Zhigang, et al. Global exponential synchronization of memristor-based recurrent neural networks with time-varying delays[J]. Neural Networks,2013,48(1): 195-203.
|
[28] |
ZHANG Guodong, SHEN Yi. New algebraic criteria for synchronization stability of chaotic memristive neural networks with time-varying delays[J]. IEEE Transactions on Neural Networks and Learning Systems,2013,24(10): 1701-1707.
|
[29] |
CHEN Jiejie, ZENG Zhigang, JIANG Ping. Global Mittag-Leffler stability and synchronization of memristor-based fractional-order neural networks[J]. Neural Networks,2014,51(1): 1-8.
|
[30] |
ZHANG Guodong, SHEN Yi. Exponential synchronization of delayed memristor-based chaotic neural networks via periodically intermittent control[J]. Neural Networks,2014,55: 1-10.
|
[31] |
BAO Haibo, PARK J H, CAO Jinde. Adaptive synchronization of fractional-order memristor-based neural networks with time delay[J]. Nonlinear Dynamics,2015,82(3): 1343-1354.
|
[32] |
CHEN Liping, QU Jianfeng, CHAI Yi, et al. Synchronization of a class of fractional order chaotic neural networks[J]. Entropy,2013,15(2): 3265-3276.
|
[33] |
ZHANG Shuo, YU Yongguang, WANG Hu. Mittag-Leffler stability of fractional order Hopfield neural networks[J]. Nonlinear Analysis: Hybrid Systems,2015,16(2): 104-121.
|