Anti-periodic solutions in a ring of four neurons with multiple delays

References

• A.P. Chen, L.H. Huang, and J.D. Cao, Existence and stability of almost periodic solution for BAM neural networks with delays, Appl. Math. Comput. 137(1) (2003), pp. 177–193. doi: 10.1016/S0096-3003(02)00095-4
   Web of Science ®Google Scholar
• Q.Y. Fan, W.T. Wang, and X.J. Yi, Anti-periodic solutions for a class of nonlinear nth-order differential equations with delays, J. Comput. Appl. Math. 230(2) (2009), pp. 762–769. doi: 10.1016/j.cam.2009.01.005
   Web of Science ®Google Scholar
• S.H. Gong, Anti-periodic solutions for a class of Cohen-Grossberg neural networks, Comput. Math. Appl. 58(2) (2009), pp. 341–347. doi: 10.1016/j.camwa.2009.03.105
   Web of Science ®Google Scholar
• S.J. Guo and L.H. Huang, Hopf bifurcating periodic orbits in a ring of neurons with delays, Phys. D 183(1C2) (2003), pp. 19–44. doi: 10.1016/S0167-2789(03)00159-3
   Web of Science ®Google Scholar
• D.W.C. Ho, J.L. Liang, and J. Lam, Global exponential stability of impulsive high-order BAM neural networks with time-varying delays, Neural Netw. 19(10) (2006), pp. 1581–1590. doi: 10.1016/j.neunet.2006.02.006
   PubMed Web of Science ®Google Scholar
• H.J. Hu and L.H. Huang, Stability and Hopf bifurcation analysis on a ring of four neurons with delays, Appl. Math. Comput. 213(2) (2009), pp. 587–599. doi: 10.1016/j.amc.2009.03.052
   Web of Science ®Google Scholar
• Z.D. Huang, L.Q. Peng, and M. Xu, Anti-periodic solutions for high-order cellular neural networks with time-varying delays, Electr. J. Differ. Equ. 2010(5) (2010), pp. 1–9.
   Google Scholar
• S. Lakshmanan, J.H. Park, T.H. Lee, H.Y. Jung, and R. Rakkiyappan, Stability criteria for BAM neural networks with leakage delays and probabilistic time-varying delays, Appl. Math. Comput. 219(17) (2013), pp. 9408–9423. doi: 10.1016/j.amc.2013.03.070
   Web of Science ®Google Scholar
• Y.K. Li, Anti-periodic solutions to impulsive shunting inhibitory cellular neural networks with distributed delays on time scales, Commun. Nonlinear Sci. Numer. Simul. 16(8) (2011), pp. 3326–3336. doi: 10.1016/j.cnsns.2010.11.004
   Web of Science ®Google Scholar
• Y.K. Li and C. Wang, Existence and global exponential stability of equilibrium for discrete-time fuzzy BAM neural networks with variable delays and impulses, Fuzzy Sets and Systems 217 (2013), pp. 62–79. doi: 10.1016/j.fss.2012.11.009
   Web of Science ®Google Scholar
• Y.K. Li and L. Yang, Anti-periodic solutions for Cohen-Grossberg neural netowrks with bounded and unbounded delays, Commun. Nonlinear Sci. Numer. Simul. 14(7) (2009), pp. 3134–3140. doi: 10.1016/j.cnsns.2008.12.002
   Web of Science ®Google Scholar
• Y.K. Li, E.L. Xu, and T.W. Zhang, Existence and stability of anti-periodic solution for a class of generalized neural networks with impulsives and arbitrary delays on time scales, J. Inequal. Appl. (2010), p. 19. Article ID 132790.
   Google Scholar
• Y.K. Li, L. Yang, and W.Q. Wu, Anti-periodic solutions for a class of Cohen-Grossberg neural networks with time-varying on time scales, Internat. J. Systems Sci. 42(7) (2011), pp. 1127–1132. doi: 10.1080/00207720903308371
   Web of Science ®Google Scholar
• B.W. Liu, Global exponential stability for BAM neural networks with time-varying delays in the leakage terms, Nonlinear Anal. Real World Appl. 14(1) (2013), pp. 559–566. doi: 10.1016/j.nonrwa.2012.07.016
   Web of Science ®Google Scholar
• D.Y. Liu, W.J. Wu, H.T. Liu, and J.W. Zhang, Anti-periodic solutions for interval general bidirectional associative memory(BAM) neural networks with impulses on time scales, J. Inf. Comput. Sci. 8(16) (2011), pp. 3847–3857.
   Google Scholar
• C.X. Ou, Anti-periodic solutions for high-order Hopfield neural networks, Comput. Math. Appl. 56(7) (2008), pp. 1838–1844. doi: 10.1016/j.camwa.2008.04.029
   Web of Science ®Google Scholar
• L.J. Pan and J.D. Cao, Anti-periodic solution for delayed cellular neural networks with impulsive effects, Nonlinear Anal. Real World Appl. 12(6) (2011), pp. 3014–3027.
   Web of Science ®Google Scholar
• G.Q. Peng and L.H. Huang, Anti-periodic solutions for shunting inhibitory cellular neural networks with continuously distributed delays, Nonlinear Anal. Real World Appl. 10(40) (2009), pp. 2434–2440. doi: 10.1016/j.nonrwa.2008.05.001
   Web of Science ®Google Scholar
• L. Peng and W.T. Wang, Anti-periodic solutions for shunting inhibitory cellular neural networks with time-varying delays in leakage terms, Neurocomputing 111 (2013), pp. 27–33. doi: 10.1016/j.neucom.2012.11.031
   Web of Science ®Google Scholar
• R. Raja and S.M. Anthoni, Global exponential stability of BAM neural networks with time-varying delays: The discrete-time case, Commun. Nonlinear Sci. Numer. Simul. 16(2) (2011), pp. 613–622. doi: 10.1016/j.cnsns.2010.04.022
   Web of Science ®Google Scholar
• R. Samidurai, R. Sakthivel, and S.M. Anthoni, Global asymptotic stability of BAM neural networks with mixed delays and impulses, Appl. Math. Comput. 212(1) (2009), pp. 113–119. doi: 10.1016/j.amc.2009.02.002
   Web of Science ®Google Scholar
• J.Y. Shao, Anti-periodic solutions for shunting inhibitory cellular neural networks with time-varying delays, Phys. Lett. A 372(30) (2008), pp. 5011–5016. doi: 10.1016/j.physleta.2008.05.064
   Web of Science ®Google Scholar
• P.L. Shi and L.Z. Dong, Existence and exponential stability of anti-periodic solutions of Hopfield neural networks with impulses, Appl. Math. Comput. 216(2) (2010), pp. 623–630. doi: 10.1016/j.amc.2010.01.095
   Web of Science ®Google Scholar
• Q.K. Song and Z.D. Wang, An analysis on existence and global exponential stability of periodic solutions for BAM neural networks with time-varying delays, Nonlinear Anal. Real World Appl. 8(4) (2007), pp. 1224–1234. doi: 10.1016/j.nonrwa.2006.07.002
   Web of Science ®Google Scholar
• Y.Y. Song, Y.Y. Han, and Y.H. Peng, Stability and Hopf bifurcation in an unidirectional ring of n neurons with distributed delays, Neurocomputing 121 (2013), pp. 442–452. doi: 10.1016/j.neucom.2013.05.015
   Web of Science ®Google Scholar
• Q. Wang, Y.Y. H. Li, L.J. Su, and B.X. Dai, Anti-periodic solutions for high-order Hopfield neural networks with impulses, Neurocomputing 138 (2014), pp. 339–346. doi: 10.1016/j.neucom.2014.01.028
   Web of Science ®Google Scholar
• X.R. Wei and Z.P. Qiu, Anti-periodic solutions for BAM neural networks with time delays, Appl. Math. Comput. 221 (2013), pp. 221–229. doi: 10.1016/j.amc.2013.06.063
   Web of Science ®Google Scholar
• A.P. Zhang, Existence and exponential stability of anti-periodic solutions for HCNNs with time-varying leakage delays, Adv. Difference Equ. 162 (2013). 10.1186/1687-1847-2013-162
   Web of Science ®Google Scholar
• Z.Q. Zhang and K.Y. Liu, Existence and global exponential stability of a periodic solution to interval general bidirectional associative memory (BAM) neural networks with multiple delays on time scales, Neural Netw. 24(5) (2011), pp. 427–439. doi: 10.1016/j.neunet.2011.02.001
   PubMed Web of Science ®Google Scholar
• Z.Q. Zhang and D.M. Zhou, Existence and global exponential stability of a periodic solution for a discrete-time interval general BAM neural networks, J. Franklin Inst. 347(5) (2010), pp. 763–780. doi: 10.1016/j.jfranklin.2010.02.007
   Web of Science ®Google Scholar
• C.R. Zhang, B.D. Zheng, and L.C. Wang, Multiple Hopf bifurcations of symmetric BAM neural network model with delay, Appl. Math. Lett. 22(4) (2009), pp. 616–622. doi: 10.1016/j.aml.2008.06.049
   Web of Science ®Google Scholar
• Z.Q. Zhang, Y. Yang, and Y.S. Huang, Global exponential stability of interval general BAM neural networks with reaction-diffusion terms and multiple time-varying delays, Neural Netw. 24(5) (2011), pp. 457–465. doi: 10.1016/j.neunet.2011.02.003
   PubMed Web of Science ®Google Scholar
• Z.Q. Zhang, W.B. Liu, and D.M. Zhou, Global asymptotic stability to a generalized Cohen-Grossberg BAM neural networks of neutral type delays, Neural Netw. 25 (2012), pp. 94–105. doi: 10.1016/j.neunet.2011.07.006
   PubMed Web of Science ®Google Scholar
• Z.Q. Zhang, K.Y. Liu, and Y. Yang, New LMI-based condition on global asymptotic stability concerning BAM neural networks of neutral type, Neurocomputing 81 (2012), pp. 24–32. doi: 10.1016/j.neucom.2011.10.006
   Web of Science ®Google Scholar