Finite-time exponential synchronization of reaction-diffusion delayed complex-dynamical networks

M. Syed Ali; L. Palanisamy; Nallappan Gunasekaran; Ahmed Alsaedi; Bashir Ahmad

doi:10.3934/dcdss.2020395

Article Contents

2021, Volume 14, Issue 4: 1465-1477. Doi: 10.3934/dcdss.2020395

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Finite-time exponential synchronization of reaction-diffusion delayed complex-dynamical networks

1.
Department of Mathematics, Thiruvalluvar University, Vellore-632115, Tamil Nadu, India
2.
Department of Mathematical Sciences, Shibaura Institute of Technology, Saitama 337-8570, Japan
3.
Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics Faculty of Science, King Abdulaziz University, P.O. Box 80257, Jeddah 21589, Saudi Arabia

^* Corresponding author: M. Syed Ali
^* Corresponding author: M. Syed Ali

Received: September 30, 2019

Revised: February 29, 2020

Early access: June 2020

Published: April 2021

This project was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, under grant no. (RG-39-130-38). The authors, therefore, acknowledge with thanks DSR technical and financial support.

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Abstract

This investigation looks at the issue of finite time exponential synchronization of complex dynamical systems with reaaction diffusion term. This reort studies complex networks consisting of $ N $ straightly and diffusively coupled networks. By building a new Lyapunov krasovskii functional (LKF), using Jensens inequality and convex algorithms approach stability conditions frameworks are determined. At last, a numerical precedent is given to demonstrate the practicality of the theoretical results.

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Mathematics Subject Classification: 34K20, 34K50, 92B20, 94D05.

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Figure 1. Error trajectories of the system in Example 1 with node 6

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References

[1]	M. S. Ali, N. Gunasekaran and R. Saravanakumar, Design of passivity and passification for delayed neural networks with markovian jump parameters via non-uniform sampled-data control, Neural Computing and Applications, 30 (2018), 595-605. doi: 10.1007/s00521-016-2682-0.
[2]	M. S. Ali, N. Gunasekaran and Q. X. Zhu, State estimation of T–S fuzzy delayed neural networks with Markovian jumping parameters using sampled-data control, Fuzzy Sets and Systems, 306 (2017), 87-104. doi: 10.1016/j.fss.2016.03.012.
[3]	M. S. Ali, N. Gunasekaran and M. E. Rani, Robust stability of Hopfield delayed neural networks via an augmented LK functional, Neurocomputing, 234 (2017), 198-204.
[4]	M. Syed Ali, K. Meenakshi, N. Gunasekaran and M. Usha, Finite-time passivity of discrete-time TS fuzzy neural networks with time-varying delays, Iranian Journal of Fuzzy Systems, 15 (2018), 93-107.
[5]	M. Syed Ali, Q. X. Zhu, S. Pavithra and N. Gunasekaran, A study on $(Q, S, R)-\gamma$-dissipative synchronisation of coupled reaction-diffusion neural networks with time-varying delays, International Journal of Systems Science, 49 (2018), 755-765. doi: 10.1080/00207721.2017.1422814.
[6]	P. Balasubramaniam and L. J. Banu, Synchronization criteria of discrete-time complex networks with time-varying delays and parameter uncertainties, Cognitive Neurodynamics, 8 (2014), 199-215. doi: 10.1007/s11571-013-9272-y.
[7]	M. Fang, Synchronization for complex dynamical networks with time delay and discrete-time information, Applied Mathematics and Computation, 258 (2015), 1-11. doi: 10.1016/j.amc.2015.01.106.
[8]	D. W. Gong, H. G. Zhang, Z. S. Wang and J. H. Liu, Synchronization analysis for complex networks with coupling delay based on T–S fuzzy theory, Applied Mathematical Modelling, 36 (2012), 6215-6224. doi: 10.1016/j.apm.2012.01.041.
[9]	N. Gunasekaran, M. Syed Ali and S. Pavithra, Finite-time $L_\infty$ performance state estimation of recurrent neural networks with sampled-data signals, Neural Processing Letters, 51 (2019), 1379-1392. doi: 10.1007/s11063-019-10114-9.
[10]	W. He and J. Cao, Exponential synchronization of hybrid coupled networks with delayed coupling, IEEE Transactions on Neural Networks, 21 (2010), 571-583.
[11]	B. N. Huang, H. G. Zhang, D. W. Gong and J. Y. Wang, Synchronization analysis for static neural networks with hybrid couplings and time delays, Neurocomputing, 148 (2015), 288-293. doi: 10.1016/j.neucom.2013.11.053.
[12]	D. H. Ji, J. H. Park, W. J. Yoo, S. C. Won and S. M. Lee, Synchronization criterion for Lur'e type complex dynamical networks with time-varying delay, Physics Letters A, 374 (2010), 1218-1227. doi: 10.1016/j.physleta.2010.01.005.
[13]	Y.-G. Kao, J.-F. Guo, C.-H. Wang and X.-Q. Sun, Delay-dependent robust exponential stability of Markovian jumping reaction-diffusion Cohen–Grossberg neural networks with mixed delays, Journal of the Franklin Institute, 349 (2012), 1972-1988. doi: 10.1016/j.jfranklin.2012.04.005.
[14]	T. H. Lee, J. H. Park, H. Y. Jung, S. M. Lee and O. M. Kwon, Synchronization of a delayed complex dynamical network with free coupling matrix, Nonlinear Dynamics, 69 (2012), 1081-1090. doi: 10.1007/s11071-012-0328-z.
[15]	J. G. Lu, Global exponential stability and periodicity of reaction–diffusion delayed recurrent neural networks with dirichlet boundary conditions, Chaos Solitons Fractals, 35 (2008), 116-125. doi: 10.1016/j.chaos.2007.05.002.
[16]	N. N. Ma, Z. B. Liu and L. Chen, Finite-time $H_\infty$ synchronization for complex dynamical networks with markovian jump parameter, Journal of Control, Automation and Electrical Systems, 30 (2019), 75-84. doi: 10.1007/s40313-018-00428-9.
[17]	F. Z. Nian and X. Y. Wang, Chaotic synchronization of hybrid state on complex networks, International Journal of Modern Physics C, 21 (2010), 457-469. doi: 10.1142/S0129183110015221.
[18]	M.-J. Park, O. M. Kwon, J. H. Park, S.-M. Lee and E.-J. Cha, Synchronization criteria of fuzzy complex dynamical networks with interval time-varying delays, Applied Mathematics and Computation, 218 (2012), 11634-11647. doi: 10.1016/j.amc.2012.05.046.
[19]	L. Scheeffer, Ueber die bedeutung der begriffe maximum und minimum iin der variationsrechnung, Mathematische Annalen, 26 (1886), 197-208. doi: 10.1007/BF01444332.
[20]	J. Shen and J. Cao, Finite-time synchronization of coupled neural networks via discontinuous controllers, Cognitive Neurodynamics, 5 (2011), 373-385. doi: 10.1007/s11571-011-9163-z.
[21]	M. Shirkavand, M. Pourgholi and A. Yazdizadeh, Robust fixed-time synchronisation of non-identical nodes in complex networks under input non-linearities, IET Control Theory & Applications, 13 (2019), 2095-2103.
[22]	A. N. Langville and W. J. Stewart, The Kronecker product and stochastic automata networks, Journal of Computational and Applied Mathematics, 167 (2004), 429-447. doi: 10.1016/j.cam.2003.10.010.
[23]	P. Park, J. W. Ko and C. Jeong, Reciprocally convex approach to stability of systems with time-varying delays, Automatica, 47 (2011), 235-238. doi: 10.1016/j.automatica.2010.10.014.
[24]	J.-A. Wang, New synchronization stability criteria for general complex dynamical networks with interval time-varying delays, Neural Computing and Applications, 28 (2017), 805-815. doi: 10.1007/s00521-015-2108-4.
[25]	J. Y. Wang, J. W. Feng, C. Xu, Y. Zhao and J. Q. Feng, Pinning synchronization of nonlinearly coupled complex networks with time-varying delays using M-matrix strategies, Neurocomputing, 177 (2016), 89-97. doi: 10.1016/j.neucom.2015.11.011.
[26]	L. Wang and Q.-G. Wang, Synchronization in complex networks with switching topology, Physics Letters A, 375 (2011), 3070-3074. doi: 10.1016/j.physleta.2011.06.054.
[27]	M.-G. Wang, X.-Y. Wang and Z.-Z. Liu, A new complex network model with hierarchical and modular structures, Chinese Journal of Physics, 48 (2010), 805-813.
[28]	Y. Xu, W. Zhou, C. Xie and D. Tong, et al., Finite-time synchronization of the complex dynamical network with non-derivative and derivative coupling, Neurocomputing, 173 (2016), 1356-1361.
[29]	X. S. Yang and J. D. Cao, Finite-time stochastic synchronization of complex networks, Applied Mathematical Modelling, 34 (2010), 3631-3641. doi: 10.1016/j.apm.2010.03.012.
[30]	X. S. Yang, J. D. Cao and J. Q. Lu, Synchronization of delayed complex dynamical networks with impulsive and stochastic effects, Nonlinear Analysis: Real World Applications, 12 (2011), 2252-2266. doi: 10.1016/j.nonrwa.2011.01.007.
[31]	X. S. Yang, J. D. Cao and Z. C. Yang, Synchronization of coupled reaction-diffusion neural networks with time-varying delays via pinning-impulsive controller, SIAM Journal on Control and Optimization, 51 (2013), 3486-3510. doi: 10.1137/120897341.
[32]	J. F. Zeng and J. D. Cao, Synchronisation in singular hybrid complex networks with delayed coupling, International Journal of Systems, Control and Communications, 3 (2011), 144-157. doi: 10.1504/IJSCC.2011.039865.
[33]	J. Zhang and Y. B. Gao, Synchronization of coupled neural networks with time-varying delay, Neurocomputing, 219 (2017), 154-162. doi: 10.1016/j.neucom.2016.09.004.
[34]	Y.-J. Zhang, S. Liu, R. Yang, Y.-Y. Tan and X. Y. Li, Global synchronization of fractional coupled networks with discrete and distributed delays, Physica A: Statistical Mechanics and its Applications, 514 (2019), 830-837. doi: 10.1016/j.physa.2018.09.129.
[35]	J. Zhou, Q. J. Wu and L. Xiang, Impulsive pinning complex dynamical networks and applications to firing neuronal synchronization, Nonlinear Dynamics, 69 (2012), 1393-1403. doi: 10.1007/s11071-012-0355-9.