Advertisement

Springer Nature is making Coronavirus research free. View research | View latest news | Sign up for updates

Anti-periodic Oscillations of Fuzzy Delayed Cellular Neural Networks with Impulse on Time Scales

  • 3 Accesses

Abstract

In this manuscript, fuzzy delayed cellular neural networks with impulse are studied. Applying time scale calculus knowledge, mathematical inequalities and constructing Lyapunov function, we establish a sufficient criterion that guarantees the existence and exponential stability of anti-periodic solutions for fuzzy delayed cellular neural networks with impulse. In addition, an example with its numerical simulations is given to illustrate our theoretical predictions.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3
Fig. 4

References

  1. 1.

    Li YK, Shu JY (2011) Anti-periodic solution to impulsive shunting inhibitory cellular neural networks with distributed delays on time scales. Commun Nonlinear Sci Numer Simul 16(8):3326–3336

  2. 2.

    Wang JL, Jiang HJ, Hu C, Ma TL (2014) Convergence behavior of delayed discrete cellular neural network without periodic coefficients. Neural Netw 53:61–68

  3. 3.

    Wang LX, Zhang JM, Shao HJ (2014) Existence and global stability of a periodic solution for a cellular neural network. Commun Nonlinear Sci Numer Simul 19(9):2983–2992

  4. 4.

    Long SJ, Xu DY (2013) Global exponential stability of non-autonomous cellular neural networks with impulses and time-varying delays. Commun Nonlinear Sci Numer Simul 18(6):1463–1472

  5. 5.

    Stamova IM, Ilarionov R (2010) On global exponential stability for impulsive cellular neural networks with time-varying delays. Comput Math Appl 59(11):3508–3515

  6. 6.

    Balasubramaniam P, Kalpana M, Rakkiyappan R (2011) Existence and global asymptotic stability of fuzzy cellular neural networks with time dealy in the leakage term and unbounded distributed delays. Circuits Syst Sig Process 30(6):1595–1616

  7. 7.

    Li YK, Chen XR, Zhao L (2009) Stability and exisence of periodic solutions to delayed Cohen–Grossberg BAM neural networks with impulses omn time scales. Neurocomputing 72(7–9):1621–1630

  8. 8.

    Li YK, Yang L, Sun LJ (2013) Existence and exponential stability of an equilibrium point for fuzzy BAM neural networks with time-varying delays in leakage terms on time scales. Adv Differ Equ 2013:218. https://doi.org/10.1186/1687-1847-2013-218

  9. 9.

    Balasubramaniam P, Ali MS, Arik S (2010) Global asymptotic stability of stochastic fuzzy cellular neural networks with multiple time-varying delays. Expert Syst Appl 37(12):7737–7744

  10. 10.

    Ali MS, Balasubramaniam P (2011) Global asymptotic stability of stochastic fuzzy cellular neural networks with multiple discrete and distributed time-varying delays. Commun Nonlinear Sci Numer Simul 16(7):2907–2916

  11. 11.

    Balasubramaniam P, Kalpana M, Rakkiyappan R (2011) State estimation for fuzzy cellular neural networks with time delay in the leakage term, discrete and unbounded distributed delays. Comput Math Appl 62(10):3959–3972

  12. 12.

    Long SJ, Xu DY (2011) Stability analysis of stochastic fuzzy cellular neural networks with time-varying delays. Neurocomputing 74(14–15):2385–2391

  13. 13.

    Balasubramaniam P, Kalpana M, Rakkiyappan R (2011) Global asymptotic stability of BAM fuzzy cellular neural networks with time delay in the leakage term, discrete and unbounded distributed delays. Math Comput Modell 53(5–6):839–853

  14. 14.

    Song QK, Cao JD (2008) Dynamical behaviors of discrete-time fuzzy cellular neural networks with variable delays and impulses. J Frankl Inst 345(1):39–59

  15. 15.

    Song QK, Wang ZD (2009) Dynamical behaviors of fuzzy reaction–diffusion periodic cellular neural networks with variable coefficients and delays. Appl Math Model 33(9):3533–3545

  16. 16.

    Yuan K, Cao JD, Deng JM (2006) Exponential stability and periodic solutions of fuzzy cellular neural networks with time-varying delays. Neurocomputing 69(13–15):1619–1627

  17. 17.

    Gan QT, Xu R, Yang PH (2012) Exponential synchronization of stochastic fuzzy cellular neural networks with time delay in the leakage term and reaction–diffusion. Commun Nonlinear Sci Numer Simul 17(4):1862–1870

  18. 18.

    Li YK, Wang C, Li X (2014) Existence and global exponential stability of almost periodic solution for high-order BAM neural networks with delays on time scales. Neural Process Lett 39(3):247–268

  19. 19.

    Li YK, Yang L (2009) Anti-periodic solutions for Cohen–Grossberg neural netowrks with bounded and unbounded dealys. Commun Nonlinear Sci Numer Simul 14(7):3134–3140

  20. 20.

    Shao JY (2008) Anti-periodic solutions for shunting inhibitory cellular neural networks with time-varying delays. Phys Lett A 372(30):5011–5016

  21. 21.

    Fan QY, Wang WT, Yi XJ (2009) Anti-periodic solutions for a class of nonlinear \(n\)th-order differential equations with delays. J Comput Appl Math 230(2):762–769

  22. 22.

    Li YK, Xu EL, Zhang TW (2010) 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 2010:132790

  23. 23.

    Gong SH (2009) Anti-periodic solutions for a class of Cohen–Grossberg neural networks. Comput Math Appl 58(2):341–347

  24. 24.

    Ou CX (2008) Anti-periodic solutions for high-order Hopfield neural networks. Comput Math Appl 56(7):1838–1844

  25. 25.

    Peng GQ, Huang LH (2009) Anti-periodic solutions for shunting inhibitory cellular neural networks with continuously distributed delays. Nonlinear Anal Real World Appl 10(40):2434–2440

  26. 26.

    Huang ZD, Peng LQ, Xu M (2010) Anti-periodic solutions for high-order cellular neural netowrks with time-varying delays. Electr J Differ Equ 2010(5):1–9

  27. 27.

    Zhang AP (2013) Existence and exponential stability of anti-periodic solutions for HCNNs with time-varying leakage delays. Adv Differ Equ 2013:162. https://doi.org/10.1186/1687-1847-2013-162

  28. 28.

    Li YK, Yang L, Wu WQ (2011) Anti-periodic solutions for a class of Cohen–Grossberg neural networks with time-varying on time scales. Int J Syst Sci 42(7):1127–1132

  29. 29.

    Li YK (2011) Anti-periodic solutions to impulsive shunting inhibitory cellular neural networks with distributed delays on time scales. Commun Nonlinear Sci Numer Simul 16(8):3326–3336

  30. 30.

    Peng L, Wang WT (2013) Anti-periodic solutions for shunting inhibitory cellular neural networks with time-varying delays in leakage terms. Neurocomputing 111:27–33

  31. 31.

    Shi PL, Dong LZ (2010) Existence and exponential stability of anti-periodic solutions of Hopfield neural networks with impulses. Appl Math Comput 216(2):623–630

  32. 32.

    Wei XR, Qiu ZP (2013) Anti-periodic solutions for BAM neural networks with time delays. Appl Math Comput 221:221–229

  33. 33.

    Huang ZD, Peng LQ, Xu M (2010) Anti-periodic solutions for high-order cellular neural networks with time-varying delays. Electr J Differ Equ 2010(5):1–9

  34. 34.

    Pan LJ, Cao JD (2011) Anti-periodic solution for delayed cellular neural networks with impulsive effects. Nonlinear Anal Real World Appl 12(6):3014–3027

  35. 35.

    Wang Q, Fang YY, Li H, Su LJ, Dai BX (2014) Anti-periodic solutions for high-order Hopfield neural networks with impulses. Neurocomputing 138:339–346

  36. 36.

    Li YK, Shu JiY (2011) Anti-periodic solutions to impulsive shunting inhibitory cellular neural networks with distributed delays on time scales. Commun Nonlinear Sci Numer Simul 16(8):3326–3336

  37. 37.

    Yang WG (2014) Periodic solution for fuzzy Cohen–Grossberg BAM neural networks with both time-varying and distributed delays and variable coefficients. Neural Process Lett 4(1):51–73

  38. 38.

    Lakshikantham V, Sivasundaram S, Kaymarkcalan B (1996) Dyanmic system on measure chains. Kluwer Academic Publishers, Boston

  39. 39.

    Aulbach B, Hilger S (1990) Linear dynamical processes with inhomogeneous time scales. Nonlinear dynamics and quantum dynamical systems. Akademie Verlage, Berlin

  40. 40.

    Hilger S (1990) Analysis on measure chains—a unfified approach to continuous and discrete calculus. RM 18(1):18–56

  41. 41.

    Bohner M, Peterson A (2003) Advances in dynamic equations on time scales. Birkhäuser, Boston

  42. 42.

    Du N, Tien L (2007) On the exponential stability of dynamic equations on time scales. J Math Anal Appl 331(2):1159–1174

  43. 43.

    Kaufmann ER, Raffoul YN (2006) Periodic solutions for a neutral nonlinear dynamical equation on a time scale. J Math Anal Appl 319(1):315–325

  44. 44.

    Lakshmikantham V, Vatsal AS (2002) Hybrid systems on time scales. J Comput Appl Math 141(1–2):227–235

  45. 45.

    Liu X, Li W (2007) Periodic solutions for dynamic equations on time scales. Nonlinear Anal Theory Methods Appl 67(5):1457–463

  46. 46.

    Xing Y, Ding W, Han M (2008) Periodic boundary value problems of integro-differential equation of Volterra type on time scales. Nonlinear Anal Theory Methods Appl 68(1):127–38

  47. 47.

    Li YK, Zhao LL, Zhang TW (2011) Global exponential stability and existence of periodic solution of impulsive Cohen–Grossberg neural networks with distributed delays on time scales. Neural Process Lett 33(1):61–81

  48. 48.

    Guseinov G (2003) Integration on time scales. J Math Anal Appl 285(1):762–769

  49. 49.

    Yang T, Yang LB (1996) The global stability of fuzzy cellular neural networks. IEEE Trans Circuits Syst I 43(10):880–883

  50. 50.

    O’regan D, Cho YJ, Chen YQ (2006) Topological degree and application. Taylor & Francis Group, New York

  51. 51.

    Yang T, Yang LB, Wu CW, Chua LO (1996) Fuzzy cellular neural network: applications. In: Proceedings of the 4th IEEE international workshop on cellular neural networks and their applications (CNNA’96), Sevilla, Spain, June 24–26

  52. 52.

    Yang T, Yang LB, Wu CW Chua LO (1996) Fuzzy cellular neural networks: theory. In: Proceedings of the 4th IEEE international workshop on cellular neural networks and their applications (CNNA’96), Sevilla, Spain, June 24–26

  53. 53.

    Laksshmikantham V, Mohapatra RN (2003) Theory of fuzzy differential equations and inclusoins. Taylor & Francis Group, New York

  54. 54.

    Xu CJ, Chen LL, Guo T (2018) Anti-periodic oscillations of bidirectional associative memory (BAM) neural networks with leakage delays. J Inequal Appl 68:1–17

  55. 55.

    Xu CJ, Li PL (2018) On anti-periodic solutions for neutral shunting inhibitory cellular neural networks with time-varying delays and D operator. Neurocomputing 275:377–382

  56. 56.

    Xu CJ (2016) Existence and exponential stability of anti-periodic solution in cellular neural networks with time-varying delays and impulsive effects. Electron J Differ Equ 2016(2):1–14

  57. 57.

    Li ZL, Dong MH, Wen SP, Hu X, Zhou P, Zeng ZG (2019) CLU-CNNs: object detection for medical images. Neurocomputing 350:53–59

  58. 58.

    Dong MH, Wen SP, Zeng ZG, Yan Z, Huang TW (2019) Sparse fully convolutional network for face labeling. Neurocomputing 331:465–472

  59. 59.

    Yan Z, Liu WW, Wen SP, Yang Y (2019) Multi-label image classification by feature attention network. IEEE Access 7(1):98005–98013

  60. 60.

    Fan YJ, Huang X, Wang Z, Li YX (2018) Nonlinear dynamics and chaos in a simplified memristor-based fractional-order neural network with discontinuous memductance function. Nonlinear Dyn 93:611–627

  61. 61.

    Fan YJ, Huang X, Shen H, Cao JD (2019) Switching event-triggered control for global stabilization of delayed memristive neural networks: an exponential attenuation scheme. Neural Netw 117:216–224

  62. 62.

    Wang Z, Wang XH, Li YX, Huang X (2017) Stability and Hopf bifurcation of fractional-order complex-valued single neuron model with time delay. Int J Bifurc Chaos 27(13):1750209

  63. 63.

    Li L, Wang Z, Li YX, Shen H, Lu JW (2018) Hopf bifurcation analysis of a complex-valued neural network model with discrete and distributed delays. Appl Math Comput 330:152–169

  64. 64.

    Wang Z, Li L, Li YY, Cheng ZS (2018) Stability and Hopf bifurcation of a three-neuron network with multiple discrete and distributed delays. Neural Process Lett 48(3):1481–1502

  65. 65.

    Fan YJ, Huang X, Wang Z, Li YX (2018) Improved quasi-synchronization criteria for delayed fractional-order memristor-based neural networks via linear feedback control. Neurocomputing 306:68–79

  66. 66.

    Wang Z, Huang X, Shi G (2011) Analysis of nonlinear dynamics and choas in a fractional order financial sytem with time delay. Comput Math Appl 62(2):1531–1539

  67. 67.

    Wang XH, Wang Z, Shen H (2019) Dynamical analysis of a discrete-time SIS epidemic model on complex networks. Appl Math Lett 94:292–299

  68. 68.

    Jia J, Huang X, Li YX, Cao J, Alsaedi A (2019) Global stabilization of fractional-order memristor-based neural networks with time delay. IEEE Trans Neural Netw Learn Syst. https://doi.org/10.1109/TNNLS.2019.2915353

  69. 69.

    Fan Y, Huang X, Li Y, Xia J, Chen G (2019) Aperiodically intermittent control for quasi-synchronization of delayed memristive neural networks: an interval matrix and matrix measure combined method. IEEE Trans Syst Man Cybern Syst 49(11):2254–2265

  70. 70.

    Li YK, Qin JL, Li B (2019) Anti-periodic solutions for quaternion-valued high-order Hopfield neural networks with time-varying delays. Neural Process Lett 49(3):1217–1237

Download references

Author information

Correspondence to Changjin Xu.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

The work is supported by National Natural Science Foundation of China (No. 61673008), Project of High-level Innovative Talents of Guizhou Province ([2016]5651), Major Research Project of The Innovation Group of The Education Department of Guizhou Province ([2017]039), Project of Key Laboratory of Guizhou Province with Financial and Physical Features ([2017]004), Foundation of Science and Technology of Guizhou Province ([2019]1051), and Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering (Changsha University of Science & Technology) (2018MMAEZD21), University Science and Technology Top Talents Project of Guizhou Province (KY[2018]047) and Guizhou University of Finance and Economics (2018XZD01).

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Xu, C., Liao, M., Li, P. et al. Anti-periodic Oscillations of Fuzzy Delayed Cellular Neural Networks with Impulse on Time Scales. Neural Process Lett (2020). https://doi.org/10.1007/s11063-020-10203-0

Download citation

Keywords

  • Fuzzy delayed cellular neural networks
  • Anti-periodic solution
  • Exponential stability
  • Time scales
  • Impulse