Abstract
This article discusses the fixed-time output synchronization of the coupled neural networks with output coupling based on impulsive effects. Two effective controls involving impulsive effects are proposed, under which sufficient conditions for output synchronization under fixed coupling weights and adaptive coupling weights are derived. Compared with the existing works, the systems investigated herein are with impulsive effects, and the settling time of synchronization is finite and independent of the initial values. Finally, a numerical example is provided to substantiate the validity and feasibility of the results.




Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Stogatz S H, Stewart I (1993) Coupled oscillators and biological synchronization. Sci Am 269(6), 102–109
Liu P, Zeng Z, Wang J (2017) Multiple mittag-leffler stability of fractional-order recurrent neural networks. IEEE Transactions Syst Man Cybern Syst 47(8): 2279-2288
Pagani G A, Aiello M (2013) The power grid as a complex network: a survey. Physica A-Stat Mech Appl 392(11), 2688–2700
Liu P, Wang J, Guo Z (2020) Multiple and complete stability of recurrent neural networks with sinusoidal activation function. IEEE Trans Neural Netw Learn Syst. https://doi.org/10.1109/TNNLS.2020.2978267
Zeng X, Wen S, Zeng Z, Huang T (2018) Design of memristor-based image convolution calculation in convolutional neural network. Neural Comput Appl 30(2), 503–508
Wen S, Xie X, Yan Z, Huang T, Zeng Z (2018) General memristor with applications in multilayer neural networks. Neural Netw 103: 142–149
Yang X, Cao J, Lu J (2012) Synchronization of Markovian coupled neural networks with nonidentical node-delays and random coupling strengths. IEEE Transactions Neural Netw Learn Syst 23(1), 60–71
Tang Y, Wong W K (2013) Distributed synchronization of coupled neural networks via randomly occurring control. IEEE Transactions Neural Netw Learn Syst 24(3), 435–447
Chen H, Shi P, Lim C (2017) Exponential synchronization for Markovian stochastic coupled neural networks of neutral-type via adaptive feedback control. IEEE Transactions Neural Netw Learn Syst28(7), 1618–1632
Wang J, Wang D, Wu H, Huang T (2019) Output synchronization of complex dynamical networks with multiple output or output derivative couplings. IEEE Transactions Cybern https://doi.org/10.1109/TCYB.2019.2912336
Wang W, Cao J (2006) Synchronization in an array of linearly coupled networks with time-varying delay. Physica A 366(1), 197–211
Lu J, Ho D W C, Liu M (2007) Globally exponential synchronization in an array of asymmetric coupled neural networks. Phys Lett A 369(5–6), 444–451
Zhang J, Gao Y (2017) Synchronization of coupled neural networks with time-varying delay. Neurocomputing 219: 154–162
Liu X, Cao J, Yu W, Song Q (2016) Nonsmooth finite-time synchronization of switched coupled neural networks. IEEE Transactions Cybern 46(10), 2360–2371
Tang Z, Park J H, Wang Y, Feng J (2020) Parameters variation-Based synchronization on derivative coupled lur’e networks. IEEE Transactions Syst Man Cybern Syst 50(12), 5395–5405
Lu B, Jiang H, Hu C, Abdurahman A (2020) Spacial sampled-data control for \(H_{\infty }\) output synchronization of directed coupled reaction-diffusion neural networks with mixed delays. Neural Netw 123: 429–440
Lou X, Cui B (2008) Synchronization of neural networks based on parameter identification and via output or state coupling J Comput Appl Math 222(2), 440–457
Wang J, Wu H, Huang T, Xu M (2018) Output Synchronization in Coupled Neural Networks With and Without External Disturbances. IEEE Transactions Control Netw Syst 5(4), 2049–2061
Lu H, Chen G (2006) Global synchronization in an array of linearly coupled delayed neural networks with an arbitrary coupling matrix. Int J Bifurc Chaos Appl Sci Eng 16(11), 3357–3368
Wang Q, Wang J (2020) Finite-Time output synchronization of undirected and directed coupled neural networks with output coupling. IEEE Transactions Netw Syst Learn Syst https://doi.org/10.1109/TNNLS.2020.2997195
Wu Y, Cao J, Li Q, Alsaedi A, Alsaadi F E (2017) Finite-time synchronization of uncertain coupled switched neural networks under asynchronous switching. Neural Netw 85: 128–139
Liu P, Zeng Z, Wang J (2020) Asymptotic and finite-Time cluster synchronization of coupled fractional-order neural networks with time delay. IEEE Transactions Netw Syst Learn Syst 31(11), 4956–4967
Wang J, Wang Q, Wu H, Huang T (2020) Finite-Time output synchronization and \(H_{\infty }\) output synchronization of coupled neural networks with multiple output couplings. IEEE Transactions Cybern https://doi.org/10.1109/TCYB.2020.2964592
Pratap A, Raja R, Cao J, Alzabut J, Huang C (2020) Finite-time synchronization criterion of graph theory perspective fractional-order coupled discontinuous neural networks. Adv Differ Equ 97: 1–24
Yang C, Xiong Z, Yang T (2020) Finite-Time synchronization of coupled inertial memristive neural networks with mixed delays via nonlinear feedback control. Neural Process Lett 51(2), 1921–1938
Lü L, He W, Han Q, Peng C (2019) Fixed-time pinning-controlled synchronization for coupled delayed neural networks with discontinuous activations. Neural Netw 116: 139–149
Zhu X, Yang X, Alsaadi F E, Hayat T (2018) Fixed-Time synchronization of coupled discontinuous neural networks with nonidentical perturbations. Neural Proces Lett 48(2), 1161–1174
Hu C, Yu J, Chen Z, Jiang H, Huang T (2017) Fixed-time stability of dynamical systems and fixed-time synchronization of coupled discontinuous neural networks. Neural Netw 89: 74–83
Lü H, He W, Han Q, Peng C (2018) Fixed-time synchronization for coupled delayed neural networks with discontinuous or continuous activations Neurocomputing 314: 143–153
Gong S, Guo Z, Wen S, Huang T (2019) Finite-time and fixed-time synchronization of coupled memristive neural networks with time delay. IEEE Transactions Cybern https://doi.org/10.1109/TCYB.2019.2953236
Zheng M, Li L, Peng H, Xiao J, Yang Y, Zhang Y, Zhao H (2018) Globally fixed-time synchronization of coupled neutral-type neural network with mixed time-varying delays. Plos One 13(1), 1–22
Ouyang D, Shao J, Jiang H, Nguang S K, Shen H T (2020) Impulsive synchronization of coupled delayed neural networks with actuator saturation and its application to image encryption. Neural Netw 128: 158–171
Karthick S A, Sakthivel R, Alzahrani F, Leelamani A (2020) Synchronization of semi-Markov coupled neural networks with impulse effects and leakage delay. Neurocomputing 386: 221–231
Lu J, Ho D W C, Cao J (2010) A unified synchronization criterion for impulsive dynamical networks. Automatica 46(7), 1215–1221
Tang Z, Park J H, Wang Y, Feng J (2020) Impulsive synchronization of derivative coupled neural networks with cluster-tree topology. IEEE Transactions Neural Sci Eng 7(3), 1788–1798
Li N, Wu X, Yang Q (2020) Fixed-time synchronization of complex dynamical network with impulsive effects. IEEE Access 8: 33072–33079
Aouiti C, Assali E A, Cherif F, Zeglaoui A (2020) Fixed-time synchronization of competitive neural networkswith proportional delays and impulsive effect Neural Comput Appl 32: 13245–13254
Jiang B, Lu J, Lou J, Qiu J (2020) Synchronization in an array of coupled neural networks with delayed impulses: average impulsive delay method Neural Netw 121: 452–460
Filippov AF (1988) Mathematics and its applicarions. Diferential equations with discontinuous right-hand side. Klower Academic Publishers. Boston
Forti M, Nistri P (2003) Global convergence of neural networks with discontinuous neuron activations. IEEE Transactions Circuits Syst Part I: Fundam Theory Appl 50(11): 1421-1435
Forti M, Nistri P, Papini D (2005) Global exponential stability and global convergence in finite time of delayed neural networks with infinite gain. IEEE Transactions Neural Netw 16(6), 1449–1463
Zhang W, Yang S, Li C, Li Z (2019) Finite-time and fixed-time synchronization of complex networks with discontinuous nodes via quantized control. Neural Process Lett 50(3), 2073–2086
Liu X, Chen T, Cao J, Lu W (2011) Dissipativity and quasisynchronization for neural networks with discontinuous activations and parameter mismatches Neural Netw 24(10), 1013–1021
Qin J, Zhang W, Gao H (2011) On pinning synchronisability of complex networks with arbitrary topological structure. Int J Syst Sci 42(9), 1559–1571
Acknowledgements
This work was supported in part by the National Natural Science Foundation of China (Grant no. 61775198, 62076222, 61703313), Henan Province University Science and Technology Innovation Talent Support Plan under Grant 20HASTIT027 and the Science and Technology Innovation Team Project of Henan Province (Grant no. 19IRTSTHN013).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflicts of interest.
Data availability
The data used to support the findings of this study are available from the corresponding author upon request.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Fang, J., Zhang, Y., Liu, P. et al. Fixed-time output synchronization of coupled neural networks with output coupling and impulsive effects. Neural Comput & Applic 33, 17647–17658 (2021). https://doi.org/10.1007/s00521-021-06349-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00521-021-06349-0