Pseudo Almost Periodic Synchronization of OVCNNs with Time-Varying Delays and Distributed Delays on Time Scales

• Shiping Shen ^[1] ; Xiaofang Meng ^[1] ; Li Yang ^[1]
  1. [1] Yunnan University of Finance and Economics
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº 1, 2024
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • This paper investigates the problem of the pseudo almost periodic synchronization in octonion-valued cellular neural networks with time-varying and distributed delays on time scales, employing a non-decomposition method. Secondly, by using the differential inequality technique on the time scale, Banach fixed point theorem, and calculus theory on the time scale are utilized to derive a sufficient condition for the existence of pseudo almost periodic solutions in the neural network on the time scale. Thirdly, the forensic method is employed to achieve the pseudo almost periodic synchronization in the network error system. Finally, a numerical example is given to illustrate the effectiveness of the results. The results obtained in this paper are new even for differential equations and difference equations.

• Referencias bibliográficas
  • 1. Chua, L.O., Yang, L.: Cellular neural networks: theory. IEEE Trans. Circuits Syst. 35(10), 1257–1272 (1988)
  • 2. Chua, L.O., Yang, L.: Cellular neural networks: applications. IEEE Trans. Circuits Syst. 35(10), 1273– 1290 (1988)
  • 3. Chua, L.O., Roska, T.: Cellular Neural Networks and Visual Computing: Foundations and Applications. Cambridge University Press, Cambridge...
  • 4. Roska, T., Chua, L.O.: Cellular neural networks with non-linear and delay-type template elements and non-uniform grids. Int. J. Circuit...
  • 5. Miller, J.P., Roska, T., Sziranyi, T., Crounse, K.R., Chua, L.O., Nemes, L.: Deblurring of images by cellular neural networks with applications...
  • 6. Werblin, F., Roska, T., Chua, L.O.: The analogic cellular neural network as a bionic eye. Int. J. Circuit Theory Appl. 23(6), 541–569 (1995)
  • 7. Vandewalle, J., Roska, T.: Guest editorial: special issue: cellular neural networks. Int. J. Circuit Theory Appl. 24(1), 3–5 (1996)
  • 8. Cao, J., Zhou, D.: Stability analysis of delayed cellular neural networks. Neural Netw. 11(9), 1601–1605 (1998)
  • 9. Li, Y.K., Xing, W., Lu, L.: Existence and global exponential stability of periodic solution of a class of neural networks with impulses....
  • 10. Li, Y.K.: Global stability and existence of periodic solutions of discrete delayed cellular neural networks. Phys. Lett. A 333(1–2), 51–61...
  • 11. Li, Y.K., Meng, X.F., Ye, Y.: Almost periodic synchronization for quaternion-valued neural networks with time-varying delays. Complexity...
  • 12. Kumar, U., Das, S., Huang, C., et al.: Fixed-time synchronization of quaternion-valued neural networks with time-varying delay. Proc....
  • 13. Wu, Z.: Multiple asymptotic stability of fractional-order quaternion-valued neural networks with timevarying delays. Neurocomputing 448,...
  • 14. Li, Y.K., Ruan, C.F., Li, B.: Existence and finite-time stability of Besicovitch almost periodic solutions of fractional-order quaternion-valued...
  • 15. Arbi, A., Tahri, N.: Stability analysis of inertial neural networks: a case of almost anti-periodic environment. Math. Methods Appl. Sci....
  • 16. Arbi, A., Tahri, N.: Almost anti-periodic solution of inertial neural networks model on time scales. In: MATEC Web of Conferences, vol....
  • 17. Arbi, A., Cao, J.D., Es-saiydy, M., Zarhouni, M., Zitane, M.: Dynamics of delayed cellular neural networks in the Stepanov pseudo almost...
  • 18. Arbi, A., Tahri, N.: New results on time scales of pseudo Weyl almost periodic solution of delayed QVSICNNs. Comput. Appl. Math. 41(6),...
  • 19. Bohner, M., Peterson, A.: Dynamic Equations on Time Scales. An Introuduction with Applications. Birkhäuser, Boston (2001)
  • 20. Hilger, S.: Analysis on measure chains—a unified approach to continuous and discrete calculus. Result Math. 18(1–2), 18–56 (1990)
  • 21. Georgiev, S.G.: Integral equations on time scales (2016)
  • 22. Al-Salih, R., Bohner, M.: Linear programming problems on time scales. Appl. Anal. Discrete Math. 12(1), 192–204 (2018)
  • 23. Al-Salih, R., Bohner, M.: Separated and state-constrained separated linear programming problems on time scales. Boletim da Sociedade Paranaense...
  • 24. Zhang, C.Y.: Pseudo-almost-periodic solutions of some differential equations. J. Math. Anal. Appl. 181(1), 62–76 (1994)
  • 25. Diagana, T.: Pseudo almost periodic solutions to some differential equations. Nonlinear Anal. Theory Methods Appl. 60(7), 1277–1286 (2005)
  • 26. Li, Y.K., Meng, X.F., Xiong, L.L.: Pseudo almost periodic solutions for neutral type high-order Hopfield neural networks with mixed time-varying...
  • 27. Li, Y.K., Meng, X.F.: Existence and global exponential stability of pseudo almost periodic solutions for neutral type quaternion-valued...
  • 28. Meng, X.F., Li, Y.K.: Pseudo almost periodic solutions for quaternion-valued high-order Hopfield neural networks with time-varying delays...
  • 29. Popa, C.A.: Octonion-valued neural networks. In: Villa, A., Masulli, P., Pons Rivero, A. (eds.) International Conference on Artificial...
  • 30. Dickson, L.E.: On quaternions and their generalization and the history of the eight square theorem. Ann. Math. 20(3), 155–171 (1919)
  • 31. Baez, J.: The octonions. Bull. Am. Math. Soc. 39(2), 145–205 (2002)
  • 32. Okubo, S.: Introduction to Octonion and Other Nonassociative Algebras in Physics. Przeglad Telekomunikacyjny-Wiadomo´sci Telekomunikacyjne,...
  • 33. Sirley, M.B., Chanyal, B.C., Matzner, R.: Yang–Millslike field theories built on division quaternion and octonion algebras. Eur. Phys....
  • 34. Popa, C.A.: Global exponential stability of octonion-valued neural networks with leakage delay and mixed delays. Neural Netw. 105(3),...
  • 35. Kandasamy, U., Rajan, R.: Hopf bifurcation of a fractional-order octonion-valued neural networks with time delays. Discrete Contin. Dyn....
  • 36. Popa, C.A.: Dissipativity of impulsive matrix-valued neural networks with leakage delay and mixed delays. Neurocomputing 405, 85–95 (2020)
  • 37. Li, Y.K., Huang, X.L.: Almost periodic oscillation of octonion-valued neural networks with delays on time scales. Int. J. Syst. Sci. 54(4),...
  • 38. Chouhan, S.S., Kumar, U., Das, S., Cao, J.D.: Fixed time synchronization of octonion valued neural networks with time varying delays....
  • 39. Masoller, C., Zanette, D.H.: Anticipated synchronization in coupled chaotic maps with delays. Phys. A Stat. Mech. Appl. 300(3–4), 359–366...
  • 40. He, W.L., Cao, J.D.: Exponential synchronization of chaotic neural networks: a matrix measure approach. Nonlinear Dyn. 55(1–2), 55–65...
  • 41. Li, Y.K., Li, C.D.: Matrix measure strategies for stabilization and synchronization of delayed BAM neural networks. Nonlinear Dyn. 84(3),...
  • 42. Duan, L., Huang, L., Fang, X.: Finite-time synchronization for recurrent neural networks with discontinuous activations and time-varying...
  • 43. Chen, W.H., Luo, S.X., Zheng, W.X.: Impulsive synchronization of reaction–diffusion neural networks with mixed delays and its application...
  • 44. Bao, H.B., Ju, H.P.: Adaptive synchronization of complex-valued neural networks with time delay. In: Eighth International Conference on...
  • 45. Li, Y.K., Wang, H.M., Meng, X.F.: Almost automorphic synchronization of quaternion-valued highorder Hopfield neural networks with time-varying...
  • 46. Li, Y.K., Li, B., Yao, S.S., et al.: The global exponential pseudo almost periodic synchronization of quaternion-valued cellular neural...
  • 47. Li, Y.K., Meng, X.F.: Synchronisation of generalised stochastic neural networks with delays and reaction–diffusion terms on timescales....
  • 48. Lu, X.D., Wang, Y.Z., Zhao, Y.G.: Synchronization of complex dynamical networks on time scales via Wirtinger-based inequality. Neurocomputing...
  • 49. Lu, X.D., Zhang, X.F., Liu, Q.R.: Finite-time synchronization of nonlinear complex dynamical networks on time scales via pinning impulsive...