Periodic oscillation for a complex-valued neural network model with discrete and distributed delays
DOI:
https://doi.org/10.14738/aivp.85.8873Keywords:
complex-valued neural network model, discrete delay, distributed delay, periodic oscillationAbstract
In this paper, a complex-valued neural network model with discrete and distributed delays is investigated under the assumption that the activation function can be separated into its real and imaginary parts. Based on the mathematical analysis method, some sufficient conditions to guarantee the existence of periodic oscillatory solutions are established. Computer simulation is given to illustrate the validity of the theoretical results.
References
(1) R. Samidurai, R. Sriraman, S. Zhu, Leakage delay-dependent stability analysis for complex-valued neural networks with discrete and distributed time-varying delays, Neurocomputing, 338 (2019) 262-273.
(2) R. Sriraman, Y. Cao, R. Samidurai, Global asymptotic stability of stochastic complex-valued neural networks with probabilistic time-varying delays, Math. Comput. Simul. 171 (2020) 103-118.
(3) P.F. Wang, X.L. Wang, H. Su, Stability analysis for complex-valued stochastic delayed networks with
Markovian switching and impulsive effects, Commun. Nonlinear Sci. Numer. Simul. 731 (2019) 35-51.
(4) R. Guo, Z. Zhang, X. Liu, C. Lin, Existence, uniqueness, and exponential stability analysis for complexvalued memristor-based BAM neural networks with time delays, Appl. Math. Comput. 311 (2017) 100-117.
(5) C.A. Popa, Global μ-stability of neutral-type impulsive complex-valued BAM neural networks with leakage delay and unbounded time-varying delays, Neurocomputing, 376 (2020) 73-94.
(6) W. Zhou, J.M. Zurada, Discrete-time recurrent neural networks with complex-valued linear threshold
neurons, IEEE Trans. Circuits Syst. II Express Briefs 56 (8) (2009) 669-673.
(7) P.F. Wang, W.Q. Zou, H. Su, J.Q. Feng, Exponential synchronization of complex-valued delayed coupled
systems on networks with aperiodically on-off coupling, Neurocomputing, 369 (2019) 155-165.
(8) Y. Kan, J.Q. Lu, J.L. Qiu, J. Kurths, Exponential synchronization of time-varying delayed complex-valued neural networks under hybrid impulsive controllers, Neural Networks, 114 (2019) 157-163.
(9) L. Li, X.H. Shi, J.L. Liang, Synchronization of impulsive coupled complex-valued neural networks with
delay: The matrix measure method, Neural Networks, 117 (2019) 285-294.
(10) D. Ding, Z. Tang, Y. Wang, Z.C. Ji, Synchronization of nonlinearly coupled complex networks: Distributed impulsive method, Chaos, Solitons and Fractals, 133 (2020) 109620.
(11) C. Hu, H.B. He, H.J. Jiang, Synchronization of complex-valued dynamic networks with intermittently adaptive coupling: A direct error method, Automatica, 112 (2020) 108675.
(12) Yu, C. Hu, H.J. Jiang, L.M. Wang, Exponential and adaptive synchronization of inertial complex-valued
neural networks: A non-reduced order and non-separation approach, Neural Networks, 124 (2020) 50-59.
(13) S. Zheng, L.G. Yuan, Nonperiodically intermittent pinning synchronization of complex-valued complex
networks with non-derivative and derivative coupling, Physica A, 525 (2019) 587-605.
(14) W. Xu, S. Zhu, X.Y. Fang, W. Wang, Adaptive anti-synchronization of memristor-based complex-valued
neural networks with time delays, Physica A, 535 (2019) 122427.
(15) Z.Y. Wang, J.D. Cao, Z.W. Cai, L.H. Huang, Periodicity and finite-time periodic synchronization of
discontinuous complex-valued neural networks, Neural Networks, 119 (2019) 249-260.
(16) R. Trabelsi, I. Jabri, F. Melgani, F. Smach, A. Bouallegue, Indoor object recognition in RGBD images
with complex-valued neural networks for visually-impaired people, Neurocomputing, 330 (2019) 94-103.
(17) Z. Wang, X. Wang, Y. Li, X. Huang, Stability and Hopf bifurcation of fractional-order complex-valued
single neuron model with time delay, Int. J. Bifurc. Chaos 27 (13) (2017) 1750209.
(18) T. Dong, X. Liao, A. Wang, Stability and Hopf bifurcation of a complex-valued neural network with two
time delays, Nonlinear Dyn. 82 (1) (2015) 1-12.
(19) C.H. Ji, Y.H. Qiao, J. Miao, L.J. Duan, Stability and Hopf bifurcation analysis of a complex-valued
Wilson-Cowan neural network with time delay, Chaos, Solitons and Fractals, 115 (2018) 45-61.
(20) C.D. Huang, J.D. Cao, M. Xiao, A. Alsaedi, T. Hayat, Bifurcations in a delayed fractional complex-valued
neural network, Appl. Math. Comput. 292 (2017) 210-227.
(21) L. Li, Z. Wang, Y.X. Li, H. Shen, J.W. Lu, Hopf bifurcation analysis of a complex-valued neural network
model with discrete and distributed delays, Appl. Math. Comput. 330 (2018) 152-169.
(22) C.R. Zhang, Z.Z. Sui, H.P. Li, Equivariant bifurcation in a coupled complex-valued neural network rings, Chaos, Solitons and Fractals, 98 (2017) 22-30.
(23) I. Ncube, Stability switching and Hopf bifurcation in a multiple-delayed neural network with distributed delay, J. Math. Anal. Appl. 407 (2013) 141-146.
(24) N. Chafee, A bifurcation problem for a functional differential equation of finitely retarded type, J. Math. Anal. Appl. 35 (1971) 312-348.
(25) C.H. Feng, R. Plamondon, An oscillatory criterion for a time delayed neural ring network model, Neural Networks 29-30 (2012) 70-79.
