Riemann-Liouville型分数阶时滞惯性复值神经网络的全局渐近同步性Global Asymptotic Synchronization for Riemann-Liouville Fractional-Order Complex-Valued Inertial Neural Networks with Time Delays
王晨,张红梅,张玮玮,张海
摘要(Abstract):
本文研究了Riemann-Liouville型分数阶时滞惯性复值神经网络的全局渐近同步问题。先引入了分数阶时滞惯性复值神经网络模型,在Riemann-Liouville型分数阶导数复合性质基础上,通过变量代换的方法将惯性系统转化为常规系统。然后,基于全局渐近同步理论和不等式技巧,得出了在新的反馈控制器下分数阶时滞惯性复值神经网络全局渐近同步的充分条件。
关键词(KeyWords): Riemann-Liouville型神经网络;时滞;全局渐近同步;复值神经网络;惯性
基金项目(Foundation): 安徽省自然科学基金项目(1908085MA01);; 安徽省高校自然科学研究重点项目(KJ2019A0573);; 安徽省高校优秀青年人才支持计划项目(gxyq2019048);; 安庆师范大学数理学院研究生学术创新项目(Y201003026)
作者(Author): 王晨,张红梅,张玮玮,张海
DOI: 10.13757/j.cnki.cn34-1328/n.2022.04.010
参考文献(References):
- [1] ZHENG M, LI L, PENG H, et al. Finite-time projective synchronization of memristor-based delay fractional-order neural networks[J]. Nonlinear Dynamics, 2017, 89(4):2641-2655.
- [2] ZHANG H, YE R, CAO J, et al. Lyapunov functional approach to stability analysis of Riemann-Liouville fractional neural networks with time-varying delays[J]. Asian Journal of Control, 2018, 20(6):1-14.
- [3] ZHANG H, YE R, CAO J, et al. Delay-independent stability of Riemann-Liouville fractional neutral-type delayed neural networks[J]. Neural Processing Letters, 2018, 47(2):427-442.
- [4] ZHANG H, YE R, LIU S, et al. LMI-based approach to stability analysis for fractional-order neural networks with discrete and distributed delays[J]. International Journal of Systems Science, 2018, 49(3):537-545.
- [5] YANG X, LI C, HUANG T, et al. Quasi-uniform synchronization of fractional-order memristor-based neural network with delay[J]. Neurocomputing, 2017, 234:205-215.
- [6] WU X, LIU S, WANG Y. Stability analysis of Riemann-Liouville fractional-order neural networks with reaction-diffusion terms and mixed time-varying delays[J]. Neurocomputing, 2021, 431:169-178.
- [7] YANG R, LIU S, LI X, et al. Consensus of fractional-order delayed multi-agent systems in Riemann-Liouville sense[J]. Neurocomputing,2020, 96:123-129.
- [8] GU Y, WANG H, YU Y. Synchronization for fractional-order discrete-time neural networks with time delays[J]. Applied Mathematics and Computation, 2020, 372:24995.
- [9] HU T, ZHANG X, ZHANG S. Global asymptotic synchronization of nonidentical fractional-order neural networks[J]. Neurocomputing,2018, 313:39-46.
- [10] LI C, CHEN G, LIAO X, et al. Hopf bifurcation and chaos in a single inertial neuron model with time delay[J]. The European Physical Journal B-Condensed Matter and Complex Systems, 2004, 41(3):337-343.
- [11] LIU Q, LIAO X, GUO S, et al. Stability of bifurcating periodic solutions for a single delayed inertial neuron model under periodic excitation[J]. Nonlinear Analysis Real World Applications, 2009, 10(4):2384-2395.
- [12] COLEMAN B, RENNINGER G. Periodic solution of certain nonlinear integral equations with a time lag[J]. Siam Journal on Applied Mathematics, 1976, 31(1):111-120.
- [13] LIU Q, LIAO X, LIU Y, et al. Dynamics of an inertial two-neuron system with time delay[J]. Nonlinear Dynamics, 2009, 58:574-609.
- [14] BABCOCK K L, WESTERVELT R M. Stability and dynamics of simple electronic neural networks with added inertia[J]. Physical D:Nonlinear Phenomena, 1987, 28(3):305-316.
- [15] KOCH C. Cable theory in neurons with active, linearized membranes[J]. Biological Cybernetics, 1984, 50(1):15-33.
- [16] HUANG C, CAO J. Impact of leakage delay on bifurcation in high-order fractional BAM neural networks[J]. Neural Networks, 2018, 98:223-235.
- [17] CHEN C, LI L, PENG H, et al. Fixed-time synchronization of inertial memristor-based neural networks with discrete delay[J]. Neural Networks, 2019, 109:81-89.
- [18] WU G, BALEANU D, ZENG S. Finite-time stability of discrete fractional delay systems:Gronwall inequality and stability criterion[J].Communications in Nonlinear ence and Numerical Simulation, 2018, 57:299-308.
- [19] WU GC, BALEANU D, XIE H P, et al. Chaos synchronization of fractional chaotic maps based on the stability condition[J]. Physical A:Statistical Mechanics and Its applications, 2016, 460:374-383.
- [20] FERRARI F A, VIANA R L, LOPES S R, et al. Phase synchronization of coupled bursting neurons and the generalized Kuramoto model[J].Neural Networks:The Official Journal of the International Neural Network Society, 2015, 66:107-118.
- [21] BAO H, CAO J. Projective synchronization of fractional-order memristor-based neural networks[J]. Neural Networks, 2015, 63:1-9.
- [22] KAN Y, LU J, QIU J, et al. Exponential synchronization of time-varying delayed complex-valued neural networks under hybrid impulsive controllers[J]. Neural Networks, 2019, 114:157-163.
- [23] PODLUBNY I. Fractional Differential Equations[M]. Academic Press, 1999.
- [24] GU Y, WANG H, YU Y. Stability and synchronization for Riemann-Liouville fractional-order time-delayed inertial neural networks[J].Neurocomputing, 2019, 340:270-280.
- [25] ZHANG W W, ZHANG H, CAO J, et al. Synchronization of delayed fractional-order complex-valued neural networks with leakage delay[J].Physical A:Statistical Mechanics and its Applications, 2020, 556:124710.
- [26] GU Y, WANG H, YU Y. Stability and synchronization for Riemann-Liouville fractional-order time-delayed inertial neural networks[J].Neurocomputing, 2019, 340:270-280.
- [27] GU Y, WANG H, YU Y. Synchronization for commensurate Riemann-Liouville fractional-order memristor-based neural networks with unknown parameters[J]. Journal of the Franklin Institut, 2020, 357:8870-8898.
- [28] BAO H, PARK J H, CAO J. Synchronization of fractional-order complex-valued neural networks with time delay[J]. Neural networks,2016:16-28.