pth Moment Exponential Stability of Impulsive Stochastic Functional Differential Equations

Qiaofeng Li; Jianli Li

Ayuda

pth Moment Exponential Stability of Impulsive Stochastic Functional Differential Equations

Qiaofeng Li ^[1] ; Jianli Li ^[1]
1. [1] Hunan Normal University
  
  Hunan Normal University
  
  China
Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 24, Nº 1, 2025
Idioma: inglés
Enlaces
- Texto completo
Resumen
- This paper centers on the exponential stability of impulsive stochastic functional differential equations. We give two related theorems. Initially, in the first theorem, we introduce a generalized Halanay inequality and use this generalized Halanay inequality to prove that impulsive stochastic functional differential equations are exponentially stable. Subsequently, in the second theorem, by Lyapunov second method, we obtain the exponential stability result for impulsive stochastic functional differential equations. Finally, the generalization and effectiveness of the results obtained are demonstrated through two examples.
Referencias bibliográficas
- 1. Alkhazzan, A., Wang, J., Tunç, C., Ding, X., Yuan, Z., Nie, Y.: On existence and continuity results of solution for multi-time scale fractional...
- 2. Li, B.: Stability of stochastic functional differential equations with impulses by an average approach. Nonlinear Anal. Hybrid Syst 29,...
- 3. Liu, B., Lu, W., Chen, T.: Generalized Halanay inequalities and their applications to neural net-works with unbounded time-varying delays....
- 4. Wang, C., Liu, X., Jiao, F., Mai, H., Chen, H., Lin, R.: Generalized Halanay inequalities and relative application to time-delay dynamical...
- 5. Huang, C., Cao, J.: On pth moment exponential stability of stochastic Cohen-Grossberg neural networks with time-varying delays. Neurocomputing...
- 6. Xu, C., Pang, Y., Liu, Z., Shen, J., Liao, M., Li, P.: Insights into COVID-19 stochastic modelling with effects of various transmission...
- 7. Xu, C., Liu, Z., Li, P., Yan, J., Yao, L.: Bifurcation mechanism for fractional-order three-triangle multi-delayed neural networks. Neural...
- 8. Xu, C., Zhao, Y., Lin, J., Pang, Y., Liu, Z., Shen, J., Qin, Y., Farman, M., Ahmad, S.: Mathematical exploration on control of bifurcation...
- 9. Xu, C., Ou, W., Pang, Y., Cui, Q., Rahman, M., Farman, M., Ahmad, S., Zeb, A.: Hopf bifurcation control of a fractional-order delayed turbidostat...
- 10. Maharajan, C., Raja, R., Cao, J., Rajchakit, G.: Novel global robust exponential stability criterion for uncertain inertial-type BAM neural...
- 11. Tunç, C., Oktan, Z.: Improved new qualitative results on stochastic delay differential equations of second order. Comput. Methods Diff....
- 12. Ruan, D., Guo, X., Shi, Y.: Generalized Halanay inequalities for stability and dissipativity of stochastic functional differential equations....
- 13. Yao, F., Cheng, P., Deng, F.: Exponential stability analysis of impulsive stochastic functional differential systems with delayed impulses....
- 14. Rajchakit, G., Chanthorn, P., Niezabitowski, M., Raja, R., Baleanu, D., Pratap, A.: Impulsive effects on stability and passivity analysis...
- 15. Kuang, H., Li, J.: Stability of stochastic functional differential equations with impulses. Appl. Math. Lett. 145, 108735 (2023)
- 16. Tian, H.: The exponential asymptotic stability of singularly perturbed delay differential equations with a bounded lag. J. Math. Anal....
- 17. Li, H., Zhou, B., Hou, M., Duan, G.: On the time-varying Halanay inequality with applications to stability analysis of time-delay systems....
- 18. Xu, H., Zhu, Q., Zheng, W.: Exponential stability of stochastic nonlinear delay systems subject to multiple periodic impulses. IEEE Trans....
- 19. Xiao, H., Li, Z., Zhang, Y., Lin, H., Zhao, Y.: A dual rumor spreading model with consideration of fans versus ordinary people. Mathematics...
- 20. Wen, L., Yu, Y., Wang, W.: Generalized Halanay inequalities for dissipativity of Volterra functional differential equations. J. Math....
- 21. Pan, L., Jin, C.: Exponential stability of impulsive stochastic functional differential equations. J. Math. Anal. Appl. 382, 672–685 (2011)
- 22. Ye, M., Li, J., Gao, D.: Some criteria on exponential stability of impulsive stochastic functional differential equations. Math. Methods...
- 23. Chinnamuniyandi, M., Chandran, S., Xu, C.: Fractional order uncertain BAM neural networks with mixed time delays: an existence and Quasi-uniform...
- 24. Iswarya,M., Raja, R., Rajchakit, G., Cao, J., Alzabut, J., Huang, C.: Existence, uniqueness and exponential stability of periodic solution...
- 25. Xia, M., Liu, L., Fang, J., Zhang, Y.: Stability analysis for a class of stochastic differential equations with impulses. Mathematics...
- 26. Tunç, O., Tunç, C.: On the asymptotic stability of solutions of stochastic differential delay equations of second order. J. Taibah Univ....
- 27. Li, P., Gao, R., Xu, C., Shen, J., Ahmad, S., Li, Y.: Exploring the impact of delay on Hopf bifurcation of a type of BAM neural network...
- 28. Zhu, Q.: Razumikhin-type theorem for stochastic functional differential equations with Lvy noise and Markov switching. Int. J. Control...
- 29. Wu, Q., Zhou, J., Xiang, L.: Impulses-induced exponential stability in recurrent delayed neural networks. Neurocomputing 74, 3204–3211...
- 30. Cui, Q., Xu, C., Ou, W., Pang, Y., Liu, Z., Li, P., Yao, L.: Bifurcation behavior and hybrid controller design of a 2D Lotka-Volterra...
- 31. Saravanakumar, R., Rajchakit, G., Ahn, C., Karimi, H.: Exponential stability, passivity, and dissipativity analysis of generalized neural...
- 32. Peng, S., Jia, B.: Some criteria on pth moment stability of impulsive stochastic functional differential equations. Statist. Probab. Lett....
- 33. Rao, R., Lin, Z., Ai, X., Wu, J.: Synchronization of epidemic systems with Neumann boundary value under delayed impulse. Mathematics 10,...
- 34. Slyn’ko, V., Tunç, C.: Stability of abstract linear switched impulsive differential equations. Automatica 107, 433–441 (2019)
- 35. Cao, W., Zhu, Q.: Razumikhin-type theorem for pth exponential stability of impulsive stochastic functional differential equations based...
- 36. Ou, W., Xu, C., Cui, Q., Pang, Y., Liu, Z., Shen, J., Baber, M., Farman, M., Ahmad, S.: Hopf bifurcation exploration and control technique...
- 37. Hu, W., Zhu, Q., Karimi, H.: Some improved Razumikhin stability criteria for impulsive stochastic delay differential systems. IEEE Trans....
- 38. Zhao, X., Deng, F.: Time-varying Halanay inequalities with application to stability and control of delayed stochastic systems. IEEE Trans....
- 39. Zhao, Y., Lin, H., Qiao, X.: Persistence, extinction and practical exponential stability of impulsive stochastic competition models with...
- 40. Wang, Z., Zhu, Q.: Two categories of new criteria of pth moment stability for switching and impulsive stochastic delayed functional differential...
- 41. Lu, Z., Zhu, Y.: Asymptotic stability in pth moment of uncertain dynamical systems with time-delays. Math. Comput. Simul. 212, 323–335...