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Articles

Almost periodic solutions for quaternion-valued shunting inhibitory cellular neural networks of neutral type with time delays in the leakage term

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Pages 2490-2505 | Received 05 Jan 2018, Accepted 22 Jul 2018, Published online: 01 Aug 2018

References

  • Aouiti, C. (2016). Neutral impulsive shunting inhibitory cellular neural networks with time-varying coefficients and leakage delays. Cognitive Neurodynamics, 10(6), 573–591. doi: 10.1007/s11571-016-9405-1
  • Balasubramaniam, P., Nagamani, G., & Rakkiyappan, R. (2011). Passivity analysis for neural networks of neutral type with Markovian jumping parameters and time delay in the leakage term. Communications in Nonlinear Science and Numerical Simulation, 16(11), 4422–4437. doi: 10.1016/j.cnsns.2011.03.028
  • Bouzerdoum, A., & Pinter, R. B. (1993). Shunting inhibitory cellular neural networks: Derivation and stability analysis. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 40(3), 215–221. doi: 10.1109/81.222804
  • Chen, X. F., Li, Z. S., Song, Q. K., Hua, J., & Tan, Y. S. (2017). Robust stability analysis of quaternion-valued neural networks with time delays and parameter uncertainties. Neural Networks, 91, 55–65. doi: 10.1016/j.neunet.2017.04.006
  • Chen, X., & Song, Q. (2013). Global stability of complex-valued neural networks with both leakage time delay and discrete time delay on time scales. Neurocomputing, 121, 254–264. doi: 10.1016/j.neucom.2013.04.040
  • Chen, X. F., Song, Q. K., Li, Z. S., Zhao, Z. J., & Liu, Y. R. (in press). Stability analysis of continuous-time and discrete-time quaternion-valued neural networks with linear threshold neurons. IEEE Transactions on Neural Networks and Learning Systems. doi:10.1109/TNNLS.2017.2704286
  • Cui, Y., Takahashi, K., & Hashimoto, M. (2013). Design of control systems using quaternionneural network and its application to inverse kinematics of robot manipulator. Proceedings of the IEEE/SICE international symposium on system integration(SII), Kobe International Conference Center, 15–17 December, 2013 Kobe, Japan, pp. 527–532.
  • Du, B., Liu, Y., Batarfi, H. A., & Alsaadi, F. E. (2016). Almost periodic solution for a neutral-type neural networks with distributed leakage delays on time scales. Neurocomputing, 173, 921–929. doi: 10.1016/j.neucom.2015.08.047
  • Du, C., Yang, C., Li, F., & Gui, W. (in press). A Novel asynchronous Control for artificial delayed Markovian jump systems via output feedback sliding mode approach. IEEE Transactions on Systems, Man, and Cybernetics: Systems. 10.1109/TSMC.2018.2815032.
  • Fan, Q. Y., & Shao, J. Y. (2010). Positive almost periodic solutions for shunting inhibitory cellular neural networks with time-varying and continuously distributed delays. Communications in Nonlinear Science and Numerical Simulation, 15(6), 1655–1663. doi: 10.1016/j.cnsns.2009.06.026
  • Fink, A. M. (1974). Almost periodic differential equations. Berlin: Springer.
  • Huang, X., & Cao, J. D. (2003). Almost periodic solution of shunting inhibitory cellular neural networks with time-varying delay. Physics Letters A, 314(3), 222–231. doi: 10.1016/S0375-9601(03)00918-6
  • Isokawa, T., Kusakabe, T., Matsui, N., & Peper, F., Quaternion neural network and its application, Lecture Notes in Artificial Intelligence, Vol. 2774. Springer; 2003, pp. 318–324.
  • Jiang, A. N. (2015). Exponential convergence for shunting inhibitory cellular neural networks with oscillating coefficients in leakage terms. Neurocomputing, 165, 159–162. doi: 10.1016/j.neucom.2015.03.005
  • Kusamichi, H., Isokawa, T., Matsui, N., Ogawa, Y., & Maeda, K. (2004). A new scheme for color night vision by quaternion neural network. Proceedings of the 2nd international conference on autonomous robots & agents (pp. 101–106). Palmerston, New Zealand.
  • Li, X. D., & Cao, J. D. (2010). Delay-dependent stability of neural networks of neutral type with time delay in the leakage term. Nonlinearity, 23(7), 1709–1726. doi: 10.1088/0951-7715/23/7/010
  • Li, F., Du, C., Yang, C., & Gui, W. (in press). Passivity-based asynchronous sliding mode control for delayed singular Markovian jump systems. IEEE Transactions on Automatic Control. doi:10.1109/TAC.2017.2776747
  • Li, L., Fang, Z., & Yang, Y. Q. (2012). A shunting inhibitory cellular neural network with continuously distributed delays of neutral type. Nonlinear Analysis Real World Applications, 13(3), 1186–1196. doi: 10.1016/j.nonrwa.2011.09.011
  • Li, Y. K., Liu, C. C., & Zhu, L. F. (2005). Global exponential stability of periodic solution for shunting inhibitory CNNs with delays. Physics Letters A, 337(1), 46–54. doi: 10.1016/j.physleta.2005.01.008
  • Li, Y., & Qin, J. (2018). Existence and global exponential stability of periodic solutions for quaternion-valued cellular neural networks with time-varying delays. Neurocomputing, 292, 91–103. doi: 10.1016/j.neucom.2018.02.077
  • Li, Y., Qin, J., & Li, B. (in press). Anti-periodic solutions for quaternion-valued high-order hopfield neural networks with time-varying delays. Neural Processing Letters. doi:10.1007/s11063-018-9867-8
  • Li, Y. K., & Shu, J. Y. (2011). Anti-periodic solutions to impulsive shunting inhibitory cellular neural networks with distributed delays on time scales. Communications in Nonlinear Science and Numerical Simulation, 16(8), 3326–3336. doi: 10.1016/j.cnsns.2010.11.004
  • Li, Y. K., & Wang, C. (2012). Almost periodic solutions of shunting inhibitory cellular neural networks on time scales. Communications in Nonlinear Science and Numerical Simulation, 17(8), 3258–3266. doi: 10.1016/j.cnsns.2011.11.034
  • Liu, B. W. (2009). Stability of shunting inhibitory cellular neural networks with unbounded time-varying delays. Applied Mathematics Letters, 22(1), 1–5. doi: 10.1016/j.aml.2007.05.012
  • Liu, B. W., & Huang, L. H. (2007a). Existence and stability of almost periodic solutions for shunting inhibitory cellular neural networks with time-varying delays. Chaos, Solitons, and Fractals, 31(1), 211–217. doi: 10.1016/j.chaos.2005.09.052
  • Liu, B. W., & Huang, L. H. (2007b). Almost periodic solutions for shunting inhibitory cellular neural networks with time-varying delays. Applied Mathematics Letters, 20(1), 70–74. doi: 10.1016/j.aml.2006.02.025
  • Liu, Y. G., You, Z. S., & Cao, L. P. (2007). Almost periodic solution of shunting inhibitory cellular neural networks with time varying and continuously distributed delays. Physics Letters A, 364(1), 17–28. doi: 10.1016/j.physleta.2006.11.075
  • Liu, Y., Zhang, D. D., Lou, J. G., Lu, J. Q., & Cao, J. D. (in press). Stability analysis of quaternion-valued neural networks: decomposition and direct approaches. IEEE Transactions on Neural Networks and Learning Systems. doi:10.1109/TNNLS.2017.2755697
  • Liu, Y., Zhang, D. D., & Lu, J. Q. (2017). Global exponential stability for quaternion-valued recurrent neural networks with time-varying delays. Nonlinear Dynamics, 87(1), 553–565. doi: 10.1007/s11071-016-3060-2
  • Liu, Y., Zhang, D. D., Lu, J. Q., & Cao, J. D. (2016). Global μ-stability criteria for quaternion-valued neural networks with unbounded time-varying delays. Information Sciences, 360, 273–288. doi: 10.1016/j.ins.2016.04.033
  • Long, Z. W. (2016). New results on anti-periodic solutions for SICNNs with oscillating coefficients in leakage terms. Neurocomputing, 171, 503–509. doi: 10.1016/j.neucom.2015.06.070
  • Matsui, N., Isokawa, T., Kusamichi, H., Peper, F., & Nishimura, H. (2004). Quaternion neural network with geometrical operators. Journal of Intelligent and Fuzzy Systems, 15(3–4), 149–164.
  • Orman, Z. (2012). New sufficient conditions for global stability of neutral-type neural networks with time delays. Neurocomputing, 97, 141–148. doi: 10.1016/j.neucom.2012.05.016
  • Ou, C. X. (2009). Almost periodic solutions for shunting inhibitory cellular neural networks. Nonlinear Analysis Real World Applications, 10(5), 2652–2658. doi: 10.1016/j.nonrwa.2008.07.004
  • Park, J. H., Kwon, O. M., & Lee, S. M. (2008). State estimation for neural networks of neutral-type with interval time-varying delays. Applied Mathematics and Computation, 203(1), 217–223. doi: 10.1016/j.amc.2008.04.025
  • Peng, L. Q., & Wang, W. T. (2013). Anti-periodic solutions for shunting inhibitory cellular neural networks with time-varying delays in leakage terms. Neurocomputing, 111(2), 27–33. doi: 10.1016/j.neucom.2012.11.031
  • Samidurai, R., Rajavel, S., Sriraman, R., Cao, J. D., Alsaedi, A., & Alsaadi, F. E. (2017). Novel results on stability analysis of neutral-type neural networks with additive time-varying delay components and leakage delay. International Journal of Control, Automation and Systems, 15(4), 1888–1900. doi: 10.1007/s12555-016-9483-1
  • Samidurai, R., Rajavel, S., Zhu, Q., Raja, R., & Zhou, H. (2016). Robust passivity analysis for neutral-type neural networks with mixed and leakage delays. Neurocomputing, 175, 635–643. doi: 10.1016/j.neucom.2015.10.103
  • Shi, P., Li, F. B., Wu, L. G., & Lim, C. C. (2017). Neural network-based passive filtering for delayed neutral-type semi-Markovian jump systems. IEEE Transactions on Neural Networks and Learning Systems, 28(9), 2101–2114.
  • Shu, H. Q., Song, Q. K., Liu, Y. R., Zhao, Z. J., & Alsaadi, F. E. (2017). Global μ-stability of quaternion-valued neural networks with non-differentiable time-varying delays. Neurocomputing, 247, 202–212. doi: 10.1016/j.neucom.2017.03.052
  • Song, Q., & Zhao, Z. (2016). Stability criterion of complex-valued neural networks with both leakage delay and time-varying delays on time scales. Neurocomputing, 171, 179–184. doi: 10.1016/j.neucom.2015.06.032
  • Sudbery, A. (1979). Quaternionic analysis. Mathematical Proceedings of the Cambridge Philosophical Society, 85(2), 199–225. doi: 10.1017/S0305004100055638
  • Tu, Z. W., Cao, J. D., Alsaedi, A., & Hayat, T. (2017). Global dissipativity analysis for delayed quaternion-valued neural networks. Neural Networks, 89, 97–104. doi: 10.1016/j.neunet.2017.01.006
  • Weera, W., & Niamsup, P. (2016). Novel delay-dependent exponential stability criteria for neutral-type neural networks with non-differentiable time-varying discrete and neutral delays. Neurocomputing, 173(3), 886–898. doi: 10.1016/j.neucom.2015.08.044
  • Xu, C. J., & Zhang, Q. M. (2015). On anti-periodic solutions of a shunting inhibitory cellular neural networks with distributed delays. Journal of Applied Mathematics and Computing, 47(1–2), 1–13. doi: 10.1007/s12190-014-0757-6
  • Zhang, D. D., Kou, K. I., Liu, Y., & Cao, J. D. (2017). Decomposition approach to the stability of recurrent neural networks with asynchronous time delays in quaternion field. Neural Networks, 94, 55–66. doi: 10.1016/j.neunet.2017.06.014
  • Zhang, H., & Shao, J. Y. (2013). Almost periodic solutions for cellular neural networks with time-varying delays in leakage terms. Applied Mathematics and Computation, 219(24), 11471–11482. doi: 10.1016/j.amc.2013.05.046

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