On Stability for Non-Instantaneous Impulsive Delay Differential Equations

• Rui Ma ^[1] ; Mengmeng Li ^[2]
  1. [1] Guizhou University

     Guizhou University

     China

     
  2. [2] Geophysical Research Institute of SINOPEC Zhongyuan Oilfield Company
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº Extra 1, 2024
• Idioma: inglés
• DOI: 10.1007/s12346-024-01146-1
• Enlaces
  • Texto completo
• Resumen

  • Many phenomena in nature can be described by establishing differential equation models. To be more practical, we extend the instantaneous impulsive delay differential equations proposed by Faria and Oliveira to the non-instantaneous impulsive delay differential equations. This paper proposes a class of non-instantaneous impulsive delay differential equations which satisfy Yorke-type condition. With the help of the definitions of stability, sufficient conditions for stability and the global asymptotic stability of the zero solution of this model are given. Finally, we give some examples and numerical simulations.

• Referencias bibliográficas
  • 1. Guglielmi, N., Iacomini, E., Viguerie, A.: Delay differential equations for the spatially-resolved simulation of epidemics with specific...
  • 2. Van den Driessche, P.: Time delay in epidemic models. IMA Vol. Math. Appl. 125, 119–128 (2002)
  • 3. Koch, G., Krzyzanski, W., Pérez-Ruixo, J.J., Schropp, J.: Modeling of delays in PKPD: Classical approaches and a tutorial for delay differential...
  • 4. Kuang, Y.: Delay Differential Equations with Applications to Population Dynamics. Academic Press, Cambridge (1993)
  • 5. MacDonald, N.: Biological Delay Systems: Linear Stability Theory. Cambridge University Press, Cambridge (1989)
  • 6. Si, Y.C., Wang, J.R.: Relative controllability of multiagent systems with pairwise different delays in states. Nonlinear Anal. Model. Control...
  • 7. Ding, X.Y., Lu, J.Q., Chen, X.Y.: Lyapunov-based stability of time-triggered impulsive logical dynamic networks. Nonlinear Anal. Hybrid...
  • 8. You, L.Y., Yang, X.Y., Wu, S.C., Li, X.D.: Finite-time stabilization for uncertain nonlinear systems with impulsive disturbance via aperiodic...
  • 9. Piper, L., Scolozzi, D., Lay-Ekuakille, A., Vergallo, P., De Franchis, E., Griffo, G.:Modeling an artificial pancreas using retarded impulsive...
  • 10. Hartung, F.: On numerical approximation of a delay differential equation with impulsive self-support condition. Appl. Math. Comput. 418,...
  • 11. Faria, T., Oliveira, J.J.: On stability for impulsive delay differential equations and application to a periodic Lasota-Wazewska model....
  • 12. Li, M.M., Wang, J.R., O’Regan, D.: Positive almost periodic solution for a noninstantaneous impulsive Lasota-Wazewska model. Bull. Iran....
  • 13. Hernández, E., O’Regan, D., Bená, M.A.: On a new class of abstract integral equations and applications. Appl. Math. Comput. 219, 2271–2277...
  • 14. Wang, J.R., Feˇckan, M.: A general class of impulsive evolution equations. Topol. Methods Nonlinear Anal. 46, 915–933 (2015)
  • 15. Wang, J.R., Zhou, Y., Lin, Z.: On a new class of impulsive fractional differential equations. Appl. Math. Comput. 242, 649–657 (2014)
  • 16. Wang, J.R., Feˇckan, M.: Non-instantaneous impulsive differential equations. In: IOP (2018)
  • 17. Li, M.M., Wang, J.R., O’Regan, D.: Stable manifolds for non-instantaneous impulsive nonautonomous differential equations. Electron. J....
  • 18. Ding, Y.L., Wang, J.R.: Periodic solutions for conformable type non-instantaneous impulsive differential equations. Electron. J. Differ....
  • 19. Ding, Y.L., O’Regan, D., Wang, J.R.: Stability analysis for conformable non-instantaneous impulsive differential equations. Bull. Iran....
  • 20. Li, M.M., Wang, J.R., O’Regan, D.: Stability of non-instantaneous impulsive systems in Hilbert spaces. Commun. Nonlinear Sci. Numer. Simul....
  • 21. Huang, C.X., Liu, B.W., Qian, C.F., Cao, J.D.: Stability on positive pseudo almost periodic solutions of HPDCNNs incorporating D operator....
  • 22. Zhao, X., Huang, C.X., Liu, B.W., Cao, J.D.: Stability analysis of delay patch-constructed Nicholson’s blowflies system. Math. Comput....
  • 23. Huang, C.X., Liu, B.W.: New studies on dynamic analysis of inertial neural networks involving nonreduced order method. Neurocomputing...
  • 24. Huang, C.X., Liu, B.W., Yang, H.D., Cao, J.D.: Positive almost periodicity on SICNNs incorporating mixed delays and D operator. Nonlinear...
  • 25. Yan, J.R.: Stability for impulsive delay differential equations. Nonlinear Anal. Theory Methods Appl. 63, 66–80 (2005)
  • 26. Liu, R., Feˇckan, M., Wang, J.R.: Ulam type stability for first-order linear and nonlinear impulsive fuzzy differential equations. Int....
  • 27. Wen, Q., Wang, J.R., O’Regan, D.: Stability analysis of second order impulsive differential equations. Qual. Theory Dyn. Syst. 21, 54...
  • 28. Mesmouli, M.B.: Stability in system of impulsive neutral functional differential equations. Mediterr. J. Math. 18, 32 (2021)
  • 29. Huang, C.D., Wang, J., Chen, X.P., Cao, J.D.: Bifurcations in a fractional-order BAM neural network with four different delays. Neural...
  • 30. Dai, Q.: Exploration of bifurcation an stability in a class of fractional-order super-double-ring neural network with two shared neurons...
  • 31. Wang, Y.: Positive solutions for fractional differential equation involving the Riemann-Stieltjes integral conditions with two parameters....
  • 32. Wang, Y., Liu, L.S., Zhang, X.G., Wu, Y.H.: Positive solutions of an abstract fractional semipositone differential system model for bioprocesses...
  • 33. Yang, Y.Q., Qi, Q.W., Hu, J.Y., Dai, J.S., Yang, C.D.: Adaptive Fault-Tolerant control for consensus of nonlinear fractional-order Multi-Agent...
  • 34. Jia, T.Y., Chen, X.Y., He, L.P., Zhao, F., Qiu, J.L.: Finite-time synchronization of uncertain fractionalorder delayed memristive neural...
  • 35. Zhao, Y.G., Sun, Y.B., Liu, Z., Wang, Y.L.: Solvability for boundary value problems of nonlinear fractional differential equations with...