On input-to-state stability for stochastic multi-group models with multi-dispersal

References

• Huang W, Cooke KL, Castillo-Chavez C. Stability and bifurcation for a multiple-group model for the dynamics of HIV/AIDS transmission. SIAM J Appl Math. 1992;52:835–854.
   Web of Science ®Google Scholar
• Thieme HR. Mathematics in population biology. Princeton: Princeton University Press; 2003.
   Google Scholar
• Lajmanovich A, Yorke JA. A deterministic model for gonorrhea in a nonhomogeneous population. Math Biosci. 1976;28:221–236.
   Google Scholar
• Feng Z, Huang W, Castillo-Chavez C. Global behavior of a multi-group SIS epidemic model with age structure. J Differ Equ. 2005;218:292–324.
   Web of Science ®Google Scholar
• Li MY, Shuai Z, Wang C. Global stability of multi-group epidemic models with distributed delays. J Math Anal Appl. 2010;361:38–47.
   Web of Science ®Google Scholar
• Ding D, Ding X. Global stability of multi-group vaccination epidemic models with delays. Nonlinear Anal-Real World Appl. 2011;12:1991–1997.
   Web of Science ®Google Scholar
• Chen H, Sun J. Stability of delayed multigroup epidemic models with group mixing and nonlinear incidence rates. Appl Math Comput. 2011;218:4391–4400.
   Web of Science ®Google Scholar
• Sun R, Shi J. Global stability of multigroup epidemic model with group mixing and nonlinear incidence rates. Appl Math Comput. 2011;218:280–286.
   Web of Science ®Google Scholar
• Wang J, Zu J, Liu X, et al. Global dynamics of a multi-group epidemic model with general relapse distribution and nonlinear incidence rate. J Biol Syst. 2012;20:235–258.
   Web of Science ®Google Scholar
• Kuniya T. Global stability of a multi-group SVIR epidemic model. Nonlinear Anal-Real World Appl. 2013;14:1135–1143.
   Web of Science ®Google Scholar
• Guo H, Li MY, Shuai Z. A graph-theoretic approach to the method of global Lyapunov functions. Proc Am Math Soc. 2008;136:2793–2802.
   Web of Science ®Google Scholar
• Li MY, Shuai Z. Global-stability problem for coupled systems of differential equations on networks. J Differ Equ. 2010;248:1–20.
   Web of Science ®Google Scholar
• Liu L, Cai W, Wu Y. Global dynamics for an SIR patchy model with susceptibles dispersal. Adv Differ Equ. 2012;131:1–11.
   Web of Science ®Google Scholar
• Muroya Y, Enatsu Y, Kuniya T. Global stability of extended multi-group sir epidemic models with patches through migration and cross patch infection. Acta Math Sci. 2013;33:341–361.
   Web of Science ®Google Scholar
• Kuniya T, Muroya Y. Global stability of a multi-group sis epidemic model for population migration. Discrete Contin Dyn Syst -- Ser B. 2014;19:1105–1118.
   Web of Science ®Google Scholar
• Wang W, Zhao X. An epidemic model in a patchy environment. Math Biosci. 2004;19:97–112.
   Web of Science ®Google Scholar
• Suo J, Sun J, Zhang Y. Stability analysis for impulsive coupled systems on networks. Neurocomputing. 2013;99:172–177.
   Web of Science ®Google Scholar
• Zhang C, Li W, Wang K. A graph-theoretic approach to stability of neutral stochastic coupled oscillators network with time-varying delayed coupling. Math Methods Appl Sci. 2014;37:1179–1190.
   Web of Science ®Google Scholar
• Li W, Su H, Wang K. Global stability analysis for stochastic coupled systems on networks. Automatica. 2011;47:215–220.
   Web of Science ®Google Scholar
• Su H, Li W, Wang K. Global stability analysis of discrete-time coupled systems on networks and its applications. Chaos. 2012;22:033135.
   PubMed Web of Science ®Google Scholar
• Zhang C, Li W, Wang K. Graph-theoretic approach to stability of multi-group models with dispersal. Discrete Contin Dyn Syst -- Ser B. 2015;20:259–280.
   Web of Science ®Google Scholar
• Zhu Q. Asymptotic stability in the pth moment for stochastic differential equations with Lévy noise. J Math Anal Appl. 2014;416:126–142.
   Web of Science ®Google Scholar
• Liu L, Zhu Q. Almost sure exponential stability of numerical solutions to stochastic delay Hopfield neural networks. Appl Math Comput. 2015;266:698–712.
   Web of Science ®Google Scholar
• Wang H, Zhu Q. Finite-time stabilization of high-order stochastic nonlinear systems in strict-feedback form. Automatica. 2015;54:284–291.
   Web of Science ®Google Scholar
• Liu L, Zhu Q. Mean square stability of two classes of theta method for neutral stochastic differential delay equations. J Comput Appl Math. 2016;305:55–67.
   Web of Science ®Google Scholar
• Yang X, Zhu Q. Corrigendum to “Stabilization in probability and mean square of controlled stochastic dynamical system with state delay”. Syst Control Lett. 2016;93:77–81.
   Web of Science ®Google Scholar
• Ji C, Jiang D, Yang Q, et al. Dynamics of a multigroup SIR epidemic model with stochastic perturbation. Automatica. 2012;48:121–131.
   Web of Science ®Google Scholar
• Yang Q, Mao X. Extinction and recurrence of multi-group SEIR epidemic models with stochastic perturbations. Nonlinear Anal-Real World Appl. 2013;14:1434–1456.
   Web of Science ®Google Scholar
• Wang Z, Fan X, Han Q. Global stability of deterministic and stochastic multigroup SEIQR models in computer network. Appl Math Model. 2013;37:8673–8686.
   Web of Science ®Google Scholar
• Liu M, Bai C, Wang K. Asymptotic stability of a two-group stochastic SEIR model with infinite delays. Commun. Nonlinear Sci Numer Simul. 2014;19:3444–3453.
   Web of Science ®Google Scholar
• Wang Z, Fan X, Jiang F, et al. Dynamics of deterministic and stochastic multi-group MSIRS epidemic models with varying total population size. Adv Differ Equ. 2014;2014:270.
   Web of Science ®Google Scholar
• Guo Y, Li Y, Ding X. Global exponential stability of multi-group models with multiple dispersal and stochastic perturbation based on graph-theoretic. Filomat. Forthcoming.
   Google Scholar
• Tsinias J. Input to state stability properties of nonlinear systems and applications to bounded feedback stabilization using saturation. ESAIM: Control Optim Calc Variations. 1997;2:57–85.
   Google Scholar
• Jiang ZP, Wang Y. Input-to-state stability for discrete-time nonlinear systems. Automatica. 2001;37:857–869.
   Web of Science ®Google Scholar
• Cai C, Teel AR. “Results on input-to-state stability for hybrid systems. In: IEEE Conference on Decision and Control-Proceedings.2005; Seville, Spain. p. 5403–5408.
   Google Scholar
• Laila DS, Astolfi A. Input-to-state stability for discrete-time-varying systems with applications to robust stabilization of systems in power form. Automatica. 2005;41:1891–1903.
   Web of Science ®Google Scholar
• Yang S, Shi B, Hao S. Input-to-state stability for discrete-time nonlinear impulsive systems with delays. Int J Robust Nonlinear Control. 2013;23:400–418.
   Web of Science ®Google Scholar
• Tai Z. Input-to-state stability for Lur’e stochastic distributed parameter control systems. Appl Math Lett. 2012;25:706–711.
   Web of Science ®Google Scholar
• Zhu Q, Cao J. Mean-square exponential input-to-state stability of stochastic delayed neural networks. Neurocomputing. 2014;131:157–163.
   Web of Science ®Google Scholar
• Zhu Q, Cao J, Rakkiyappan R. Exponential input-to-state stability of stochastic Cohen-Grossberg neural networks with mixed delays. Nonlinear Dyn. 2015;79:1085–1098.
   Web of Science ®Google Scholar
• Xu Y, Luo W, Zhong K, et al. Mean square input-to-state stability of a general class of stochastic recurrent neural networks with Markovian switching. Neural Comput Appl. 2014;25:1657–1663.
   Web of Science ®Google Scholar
• Zhao F, Zhang Q, Yan XG, et al. Stochastic input-to-state stability and H∞ filtering for a class of stochastic nonlinear systems. Appl Math Comput. 2014;227:672–686.
   Web of Science ®Google Scholar
• Yao F, Qiu L, Shen H. On input-to-state stability of impulsive stochastic systems. J Frankl Inst-Eng Appl Math. 2014;351:4636–4651.
   Web of Science ®Google Scholar
• Ai Z, Zong G. Finite-time stochastic input-to-state stability of impulsive switched stochastic nonlinear systems. Appl Math Comput. 2014;245:462–473.
   Web of Science ®Google Scholar
• Gao S, Wu B. On input-to-state stability for stochastic coupled control systems on networks. Appl Math Comput. 2015;262:90–101.
   Web of Science ®Google Scholar
• Sontag ED. Smooth stabilization implies coprime factorization. IEEE Trans Autom Control. 1989;34:435–443.
   Web of Science ®Google Scholar
• Sontag ED, Wang Y. On characterizations of the input-to-state stability property. Syst Control Lett. 1995;24:351–359.
   Web of Science ®Google Scholar
• Sontag ED, Wang Y. New characterizations of input to state stability. IEEE Trans Autom Control. 1996;41:1283–1294.
   Web of Science ®Google Scholar
• Zhang C, Li W, Su H, et al. A graph-theoretic approach to boundedness of stochastic Cohen--Grossberg neural networks with Markovian switching. Appl Math Comput. 2013;219:9165–9173.
   Web of Science ®Google Scholar
• Zhang C, Li W, Wang K. Boundedness for network of stochastic coupled van der Pol oscillators with time-varying delayed coupling. Appl Math Model. 2013;37:5394–5402.
   Web of Science ®Google Scholar
• Wang J, Zhang X, Li W. Periodic solutions of stochastic coupled systems on networks with periodic coefficients. Neurocomputing. 2016;205:360–366.
   Web of Science ®Google Scholar
• West DB. Introduction to graph theory. Upper Saddle River: Prentice Hall; 1996.
   Google Scholar
• Mao X, Yuan C. Stochastic differential equations with Markovian switching. London: Imperial College Press; 2006.
   Google Scholar