Global \(O(t^{-\alpha})\) synchronization of fractional-order non-autonomous neural network model with time delays through centralized data-sampling approach. (English) Zbl 1448.93117
Summary: This paper aims to investigate the global \(O(t^{-\alpha})\) synchronization of a class of fractional-order non-autonomous neural networks with time delay. Using centralized data-sampling principle and the theory of fractional differential equations, sufficient criteria for the \(O(t^{-\alpha})\) synchronization is derived. Centralized data-sampling control is applied in the drive-response-based coupled neural networks to achieve global \(O(t^{-\alpha})\) synchronization. It is a more effective strategy as it gives better control performance. Numerical examples are also given to illustrate the validity of the theoretical result.
MSC:
| 93B70 | Networked control |
| 93C57 | Sampled-data control/observation systems |
| 26A33 | Fractional derivatives and integrals |
| 34D06 | Synchronization of solutions to ordinary differential equations |
Keywords:
non-autonomous system; delay; \(O(t^{-\alpha})\) synchronization; centralized data-sampling controlReferences:
| [1] | Podlubny, I., Fractional Differential Equations (1999), San Diego: Academic Press, San Diego · Zbl 0924.34008 |
| [2] | Kinh, Ct; Hien, Lv; Ke, Td, Power-rate synchronization of fractional-order nonautonomous neural networks with heterogeneous proportional delays, Neural Process. Lett., 47, 1, 139-151 (2018) · doi:10.1007/s11063-017-9637-z |
| [3] | Hilfer, R., Applications of Fractional Calculus in Physics (2000), Singapore: World Scientific York, Singapore · Zbl 0998.26002 · doi:10.1142/3779 |
| [4] | Zalp, No; Demirci, E., A fractional order SEIR model with vertical transmission, Math. Comput. Modell., 54, 1-2, 1-6 (2011) · Zbl 1225.34011 |
| [5] | Laskin, N., Fractional market dynamics, Physica A, 287, 3-4, 482-492 (2000) · doi:10.1016/S0378-4371(00)00387-3 |
| [6] | Kilbas, Aa; Srivastava, Hm; Trujillo, Jj, Theory and Application of Fractional Differential Equations (2006), New York: Elsevier, New York · Zbl 1092.45003 |
| [7] | Ahmeda, E.; Elgazzar, As, On fractional order differential equations model for nonlocal epidemics, Physica A, 379, 607-614 (2007) · doi:10.1016/j.physa.2007.01.010 |
| [8] | Higgs, Mh; Spain, Wj; Fairhall, Al, Fractional differentiation by neocortical pyramidal neurons, Nat. Neurosci., 11, 1335-1342 (2008) · doi:10.1038/nn.2212 |
| [9] | Zhang, J.E.: Centralized Data-Sampling Approach for Global \(O(t^{-\alpha })\) Synchronization of Fractional-Order Neural Networks with Time Delays, Discrete Dynamics in Nature and Society, vol. 2017, Article ID 6157292 · Zbl 1369.92008 |
| [10] | Chen, B.; Chen, J., Global \(O(t^{-\alpha })\) stability and global asymptotical periodicity for a non-autonomous fractional-order neural networks with time-varying delays, Neural Netw., 73, 47-57 (2016) · Zbl 1398.34095 · doi:10.1016/j.neunet.2015.09.007 |
| [11] | Caponetto, R.; Fortuna, L.; Porto, D., Bifurcation and chaos in noninteger order cellular neural networks, Int. J. Bifurc. Chaos, 8, 1527-1539 (1998) · Zbl 0936.92006 · doi:10.1142/S0218127498001170 |
| [12] | Arena, P.; Fortuna, L.; Porto, D., Chaotic behavior in noninteger-order cellular neural networks, Phys. Rev. E, 61, 776-781 (2000) · doi:10.1103/PhysRevE.61.776 |
| [13] | Pecora, L.; Carroll, T., Synchronization in chaotic system, Phys. Rev. Lett., 64, 821-824 (1990) · Zbl 0938.37019 · doi:10.1103/PhysRevLett.64.821 |
| [14] | Chao, Wr; Dong, Hx; Ping, Cl, Finite-time stability of fractional-order neural networks with delay, Commun. Theor. Phys., 60, 189-193 (2013) · Zbl 1284.92016 · doi:10.1088/0253-6102/60/2/08 |
| [15] | Chen, J.; Zeng, Z.; Jiang, P., Global Mittag-Leffler stability and synchronization of memristor-based fractional-order neural networks, Neural Netw., 51, 1-8 (2014) · Zbl 1306.34006 · doi:10.1016/j.neunet.2013.11.016 |
| [16] | Bao, H.; Cao, J., Projective synchronization of fractional-order memristor-based neural networks, Neural Netw., 63, 1-9 (2015) · Zbl 1323.93036 · doi:10.1016/j.neunet.2014.10.007 |
| [17] | Rakkiyappan, R.; Velmurugan, G.; Cao, J., Finite-time stability analysis of fractional-order complex-valued memristor-based neural networks with time delays, Nonlinear Dyn., 78, 4, 2823-2836 (2014) · Zbl 1331.34154 · doi:10.1007/s11071-014-1628-2 |
| [18] | Chen, Lp; Wu, Rc; Cao, J.; Liu, Jb, Stability and synchronization of memristor-based fractional-order delayed neural networks, Neural Netw., 71, 37-44 (2015) · Zbl 1398.34096 · doi:10.1016/j.neunet.2015.07.012 |
| [19] | Carroll, Tl; Pecora, Lm, Synchronizing chaotic systems, IEEE Trans. Circuits Syst. I Fundam. Theory Appl., 38, 4, 453-456 (1991) · doi:10.1109/31.75404 |
| [20] | Chen, Wh; Wang, Z.; Lu, X., On sampled-data control formaster-slave synchronization of chaotic Lur’e systems, IEEE Trans. Circuits Syst. II Express Br., 59, 8, 515-519 (2012) · doi:10.1109/TCSII.2012.2204114 |
| [21] | Zhang, J.: Centralized and decentralized data-sampling principles for outer-synchronization of fractional-order neural networks. Complexity 2017, 11 (2017) (Article ID 6290646) · Zbl 1367.93356 |
| [22] | Dashkovskiy, S.; Pavlichkov, S., Constructive design of adaptive controllers for nonlinear MIMO systems with arbitrary switchings, IEEE Trans. Autom. Control, 61, 7, 2001-2007 (2016) · Zbl 1359.93223 · doi:10.1109/TAC.2015.2491679 |
| [23] | Pyrkin, A.A., Bobtsov, A.A.: Adaptive controller for linear systemwith input delay and output disturbance. In: Proceedings of the 52nd IEEE Conference on Decision and Control (CDC ’13), vol. 61, pp. 4229-4234. IEEE, Florence (2013) · Zbl 1359.93232 |
| [24] | Azzaro, Je; Veiga, Ra, Slidingmode controller with neural network identification, IEEE Lat. Am. Trans., 13, 12, 3754-3757 (2015) · doi:10.1109/TLA.2015.7404904 |
| [25] | Gu, Y.; Yu, Y.; Hu Wang, H., Synchronization for fractional-order time-delayed memristor-based neural networks with parameter uncertainty, J Frankl. Inst., 353, 3657-3684 (2016) · Zbl 1347.93013 · doi:10.1016/j.jfranklin.2016.06.029 |
| [26] | Das, P.; Das, P.; Kundu, A., Delayed feedback controller based finite time synchronization of discontinuous neural networks with mixed time-varying delays, Neural Process. Lett., 49, 693-709 (2018) · doi:10.1007/s11063-018-9850-4 |
| [27] | Das, A.; Das, P.; Roy, Ab, Chaos in a three-dimensional general model of neural network, Int. J. Bifurc. Chaos, 12, 10, 2271-2281 (2002) · Zbl 1043.37512 · doi:10.1142/S0218127402005820 |
| [28] | Das, P., Kundu, A.: Global stability, bifurcation, and chaos control in a delayed neural network model. Adv. Artif. Neural Syst. 2014, 8 (2014) (Article ID 369230) |
| [29] | Das, P.; Kundu, A., Bifurcation and chaos in delayed cellular neural network model, J. Appl. Math. Phys., 2, 219-224 (2014) · doi:10.4236/jamp.2014.25027 |
| [30] | Kundu, A., Das, P.: Global Stability and Chaos-Control in Delayed N-Cellular Neural Network Model, Applied Mathematics, Springer Proceedings in Mathematics & Statistics, vol. 146. Springer, New Delhi |
| [31] | Cong, Nd; Tuan, Ht, Existence, uniqueness, and exponential boundedness of global solutions to delay fractional differential equations, Mediterr. J. Math., 14, 193 (2017) · Zbl 1379.34071 · doi:10.1007/s00009-017-0997-4 |
| [32] | Kaslik, E.; Sivasundaram, S., Dynamics of Fractional-Order Neural Networks (2011), San Jose: IJCNN, San Jose · doi:10.1109/IJCNN.2011.6033277 |
| [33] | Anastasio, T., The fractional-order dynamics of brainstem vestibulo-oculomotor neurons, Biol. Cybern., 72, 69-79 (1994) · doi:10.1007/BF00206239 |
| [34] | Yang, Z.; Cao, J., Initial value problems for arbitrary order fractional differential equations with delay, Commun. Nonlinear Sci. Numer. Simul., 18, 11, 2993-3005 (2013) · Zbl 1329.34122 · doi:10.1016/j.cnsns.2013.03.006 |
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