Exponential synchronization of 2D cellular neural networks with boundary feedback

References

• Ambrosio, B., Aziz-Alaoui, M. A. (2013). Synchronization and control of a network of coupled reaction-diffusion systems of generalized FitzHugh-Nagumo type. ESAIM: Proc. 39: 15–24. doi:10.1051/proc/201339003.
   Google Scholar
• Arenas, A., Díaz-Guilera, A., Kurths, J., Moreno, Y., Zhou, C. (2008). Synchronization in complex networks. Phys. Rep. 469(3): 93–153. doi:10.1016/j.physrep.2008.09.002.
   Web of Science ®Google Scholar
• Chow S.-N., Mallet-Paret, J. (1995). Pattern formation and spatial chaos in lattice dynamical systems. II. IEEE Trans. Circuits Syst. I: Fundam. Theory Appl. 42(10):752–756. doi:10.1109/81.473584.
   Google Scholar
• Chua, L. O., Yang, L. (1988). Cellular neural networks: Applications. IEEE Trans. Circuits Syst. 35 (10):1273–1290. doi:10.1109/31.7601.
   Google Scholar
• Indolia, S., Goswami, A. K., Mishra, S. P., Asopa, P. (2018). Conceptual understanding of convolutional neural network- A deep learning approach. Proced. Comput. Sci. 132:679–688. doi:10.1016/j.procs.2018.05.069.
   Google Scholar
• Pecora, L. M., Carroll, T. L. (1990). Synchronization in chaotic systems. Phys. Rev. Lett. 64(8):821–824. doi:10.1103/PhysRevLett.64.821. 10042089
   PubMed Web of Science ®Google Scholar
• Pikovsky, A., Rosenblum, M., Kurths, J. (2002). Synchronization: A Universal Concept in Nonlinear Sciences. Cambridge, UK: Cambridge University Press.
   Google Scholar
• Chua, L. O., Yang, L. (1988). Cellular neural networks: Theory. IEEE Trans. Circuits Syst. 35(10):1257–1272. doi:10.1109/31.7600.
   Google Scholar
• Chua, L. O., Hasler, M., Moschytz, G. S., Neirynck, J. (1995). Autonomous cellular neural networks: a unified paradigm for pattern formation and active wave propagation. IEEE Trans. Circuits Syst. I: Fundam. Theory Appl. 42(10):559–577. doi:10.1109/81.473564.
   Google Scholar
• Chua, L. O., Roska, T. (1993). The CNN paradigm. IEEE Trans. Circuits Syst. I: Fundam. Theory Appl. 40(3):147–156. doi:10.1109/81.222795.
   Google Scholar
• Chow, S.-N., Mallet-Paret, J. (1995). Pattern formation and spatial chaos in lattice dynamical systems. I. IEEE Trans. Circuits Syst. I: Fundam. Theory Appl. 42(10):746–751. doi:10.1109/81.473583.
   Google Scholar
• Chua, L. O., Roska, T. (2002). Cellular Neural Networks and Visual Computing. Cambridge, UK: Cambridge University Press.
   Google Scholar
• Han, X., Kloeden, P. E. (2019). Asymptotic behavior of a neural field lattice model with a Heaviside operator. Phys. D: Nonlinear Phenom. 389:1–12. doi:10.1016/j.physd.2018.09.004.
   Web of Science ®Google Scholar
• Slavova, A. (2003). Cellular Neural Networks: Dynamics and Modeling. Dordrecht: Springer Science and Business Media.
   Google Scholar
• Gupta, M. M., Jin, L., Homma, N. (2003). Static and Dynamic Neural Networks: From Fundamentals to Advanced Theory. New York, NY: Wiley.
   Google Scholar
• Li, H. (2014). Celluar neural networks model on real estate investment systems and it’s stability and chaos synchronization. Open Autom. Control Syst. J. 6(1):200–202. doi:10.2174/1874444301406010200.
   Google Scholar
• Serrano-Guerrero, H. (2010). Chaotic synchronization in star coupled networks of three-dimensional cellular neural networks and its applications in communications. Int. J. Nonlinear Sci. Numer. Simul. 11:571–580.
   Web of Science ®Google Scholar
• Slavova, A. (2000). Applications of some mathematical methods in the analysis of cellular neural networks. J.Comput. Appl. Math. 114(2):387–3404. doi:10.1016/S0377-0427(99)00277-0.
   Web of Science ®Google Scholar
• Wu, C. W. (2007). Synchronization in Complex Networks of Nonlinear Dynamical Systems. Hackensack, NJ: World Scientific.
   Google Scholar
• Skrzypek, L., You, Y. (2021). Feedback synchronization of FHN cellular neural networks. Discr. Contin. Dyn. Syst.- B 26(12):6047. doi:10.3934/dcdsb.2021001.
   Google Scholar
• Fitzhugh, R. (1961). Impulses and physiological states in theoretical models of nerve membrane. Biophys. J. 1(6):445–466. doi:10.1016/s0006-3495(61)86902-6. 19431309
   PubMed Web of Science ®Google Scholar
• Wu, C. W., Chua, L. O. (1994). A unified framework for synchronization and control of dynamical systems. Int. J. Bifurc. Chaos 4(4):979–998. doi:10.1142/S0218127494000691.
   Web of Science ®Google Scholar
• Ibrahim, M. M., Jung, I. H. (2019). Complex synchronization of a ring-structured network of FitzHugh-Nagumo neurons with single-and dual-state gap junctions under ionic gates and external electrical disturbance. IEEE Access. 7:57894–5906. doi:10.1109/ACCESS.2019.2913872.
   Web of Science ®Google Scholar
• Yong, Z., Su-Hua, Z., Tong-Jun, Z., Hai-Long, A., Zhen-Dong, Z., Ying-Rong, H., Hui, L., Yu-Hong, Z. (2008). The synchronization of FitzHugh–Nagumo neuron network coupled by gap junction. Chin Phys. B 17(6):2297–2303. doi:10.1088/1674-1056/17/6/061.
   Web of Science ®Google Scholar
• Qui∼ninao, C., Touboul, J. D. (2020). Clamping and synchronization in the strongly coupled FitzHugh–Nagumo model. SIAM J. Appl. Dyn. Syst. 19(2):788–827. doi:10.1137/19M1283884.
   Web of Science ®Google Scholar
• Wei, D. Q., Luo, X. S., Zou, Y. L. (2008). Firing activity of complex space-clamped FitzHugh-Nagumo neural networks. Eur. Phys. J. B 63 (2):279–282. doi:10.1140/epjb/e2008-00227-5.
   Web of Science ®Google Scholar
• Wang, Z., Zhou, D., Ma, D., Lun, S. (2012). Global asymptotic synchronization of coupled interconnected recurring neural networks via pinning control. In: Wang, J., Yen, G. G., Polycarpou, M. M., eds. LNCS, 7367, Part I. Berlin: Springer-Verlag, 302–311.
   Google Scholar
• Zhan, M., Cao, J., Wu, Y. (2007). Chaos synchronization in coupled systems by applying pinning control. Phys. Rev. E. 76:36203.
   Web of Science ®Google Scholar
• Botmart, T., Weera, W. (2013). Guaranteed cost control for exponential synchronization of cellular neural networks with mixed time-varying delays via hybrid feedback control. Abstr. Appl. Anal. 2013:175796. doi:10.1155/2013/175796.
   Google Scholar
• Cheng, C., Liao, T., Hwang, C. (2005). Exponential synchronization of a class of chaotic neural networks. Chaos, Solit. Fract. 24(1):197–206. doi:10.1016/S0960-0779(04)00566-1.
   Web of Science ®Google Scholar
• Gao, X., Zhong, S., Gao, F. (2009). Exponential synchronization of neural networks with time-varying delays. Nonlinear Anal.: Theory, Methods Appl. 71(5-6):2003–2011. doi:10.1016/j.na.2009.01.243.
   Web of Science ®Google Scholar
• Li, X., Bohner, M. (2010). Exponential synchronization of chaotic neural networks with mixed delays and impulsive effects via output coupling with delay feedback. Math. Comput. Model. 52(5-6):643–653. doi:10.1016/j.mcm.2010.04.011.
   Google Scholar
• Yu, J., Hu, C., Jiang, H., Teng, Z. (2011). Exponential synchronization of Cohen–Grossberg neural networks via periodically intermittent control. Neurocomputing 74(10):1776–1782. doi:10.1016/j.neucom.2011.02.015.
   Web of Science ®Google Scholar
• Farid, Y., Bigdeli, N., Afshar, K. (2012). Anti-synchronization of chaotic neural networks with time-varying delays via linear matrix inequality. Int. J.Phys. Sci. 7(2):273–280.
   Google Scholar
• Grassi, G., Mascolo, S. (1999). Synchronizing high dimensional chaotic systems via eigenvalue placement with application to cellular neural networks. Int. J. Bifurc. Chaos 9(4):705–711. doi:10.1142/S0218127499000493.
   Web of Science ®Google Scholar
• Lee, T. H., Park, J. H., Ji, D. H., Kwon, O. M., Lee, S. M. (2012). Guaranteed cost synchronization of a complex dynamical network via dynamic feedback control. Appl. Math. Comput. 218(11):6469–6481. doi:10.1016/j.amc.2011.11.112.
   Web of Science ®Google Scholar
• Phan, C., Skrzypek, L., You, Y. (2022). Dynamics and synchronization of complex neural networks with boundary coupling. Anal. Math. Phys. 12(33):1–18. doi:10.1007/s13324-021-00613-1.
   Google Scholar
• Phan, C., You, Y. (2020). Synchronization of boundary coupled Hindmarsh–Rose neuron network. Nonlinear Anal.: Real World Appl. 55:103139. doi:10.1016/j.nonrwa.2020.103139.
   Web of Science ®Google Scholar
• Skrzypek, L., You, Y. (2021). Dynamics and synchronization of boundary coupled FitzHugh-Nagumo neural networks. Appl. Math. Comput. 388:125545. doi:10.1016/j.amc.2020.125545.
   Web of Science ®Google Scholar
• Sell, G., You, Y. (2002). Dynamics of Evolutionary Equations. New York: Springer-Verlag.
   Google Scholar