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Stability analysis for discrete-time coupled systems with multi-diffusion by graph-theoretic approach and its application
1. | Department of Mathematics, Harbin Institute of Technology at Weihai, Weihai 264209, China, China, China |
References:
[1] |
J. Wang, J. Zu, X. Liu, G. Huang and J. Zhang, Global dynamics of a multi-group epidemic model with general relapse distribution and nonlinear incidence rate, J. Biol. Syst., 20 (2012), 235-258.
doi: 10.1142/S021833901250009X. |
[2] |
H. Shu, D. Fan and J. Wei, Global stability of multi-group SEIR epidemic models with distributed delays and nonlinear transmission, Nonlinear Anal. RWA, 13 (2012), 1581-1592.
doi: 10.1016/j.nonrwa.2011.11.016. |
[3] |
C. Ji, D. Jiang, Q. Yang and N. Shi, Dynamics of a multigroup SIR epidemic model with stochastic perturbation, Automatica, 48 (2012), 121-131.
doi: 10.1016/j.automatica.2011.09.044. |
[4] |
H. Chen and J. Sun, Global stability of delay multigroup epidemic models with group mixing and nonlinear incidence rates, Appl. Math. Comput., 218 (2011), 4391-4400.
doi: 10.1016/j.amc.2011.10.015. |
[5] |
R. Sun and J. Shi, Global stability of multigroup epidemic model with group mixing and nonlinear incidence rates, Appl. Math. Comput., 218 (2011), 280-286.
doi: 10.1016/j.amc.2011.05.056. |
[6] |
M. Y. Li, Z. Shuai and C. Wang, Global stability of multi-group epidemic models with distributed delays, J. Math. Anal. Appl., 361 (2010), 38-47.
doi: 10.1016/j.jmaa.2009.09.017. |
[7] |
Y. Muroya, Y. Enatsu and T. Kuniya, Global stability for a multi-group SIRS epidemic model with varying population sizes, Nonlinear Anal. RWA, 14 (2013), 1693-1704.
doi: 10.1016/j.nonrwa.2012.11.005. |
[8] |
J. Epperlein, S. Siegmund and P. Stehík, Evolutionary games on graphs and discrete dynamical systems, J. Difference Eq. Appl., 21 (2015), 72-95.
doi: 10.1080/10236198.2014.988618. |
[9] |
M. Y. Li and Z. Shuai, Global-stability problem for coupled systems of differential equations on networks, J. Differ. Equ., 248 (2010), 1-20.
doi: 10.1016/j.jde.2009.09.003. |
[10] |
S. Elaydi, An Introduction to Difference Equations, 3rd ed, (Springer, New York, 2004). |
[11] |
G. Barlev, M. Girvan and E. Ott, Map model for synchronization of systems of many coupled oscillators, Chaos, 20 (2010), 023109.
doi: 10.1063/1.3357983. |
[12] |
M. Lazar, W. P. M. H. Heemels and A. R. Teel, Lyapunov functions, stability and input-to-state stability subtleties for discrete-time discontinuous systems, IEEE Trans. Autom. Control., 54 (2009), 2421-2425.
doi: 10.1109/TAC.2009.2029297. |
[13] |
J. Q. Qiu, K. F. Lu, P. Shi and M. S. Mahmoud, Robust exponential stability for discrete-time interval BAM neural networks with delays and Markovian jump parameters, Int. J. Adapt. Control., 24 (2010), 760-785.
doi: 10.1002/acs.1171. |
[14] |
M. S. Peng and X. Z. Yang, New stability criteria and bifurcation analysis for nonlinear discrete-time coupled loops with multiple delays, Chaos, 20 (2010), 013125, 11pp.
doi: 10.1063/1.3339857. |
[15] |
S. V. Naghavi and A. A. Safavi, Novel synchronization of discrete-time chaotic systems using neural network observer, Chaos, 18 (2008), 033110, 9pp.
doi: 10.1063/1.2959140. |
[16] |
J. D. Cao and J. Q. Lu, Adaptive synchronization of neural networks with or without time-varying delay, Chaos, 16 (2006), 013133, 6pp.
doi: 10.1063/1.2178448. |
[17] |
H. Su, W. Li and K. Wang, Global stability of discrete-time coupled systems on networks and its applications, Chaos, 22 (2012), 033135, 11pp.
doi: 10.1063/1.4748851. |
[18] |
C. Zhang, W. Li and K. Wang, Graph theory-based approach for stability analysis of stochastic coupled systems with Lévy noise on networks, IEEE Trans. Neural Netw. Learn. Syst., 26 (2014), 1698-1709.
doi: 10.1109/TNNLS.2014.2352217. |
[19] |
F. M. Atay and $\ddot Q$. Karabacak, Stability of coupled map networks with delays, SIAM J. Appl. Dyn. Syst., 5 (2006), 508-527.
doi: 10.1137/060652531. |
[20] |
H. Guo, M. L. Li and Z.Shuai, A graph-theoretic approach to the method of global Lyapunov functions, Proc. Amer. Math. Soc., 136 (2008), 2793-2802.
doi: 10.1090/S0002-9939-08-09341-6. |
[21] |
C. Zhang, W. Li and K. Wang, Boundedness for network of stochastic coupled van der Pol oscillators with time-varying delayed coupling, Appl. Math. Model., 37 (2013), 5394-5402.
doi: 10.1016/j.apm.2012.10.032. |
[22] |
C. Zhang, W. Li and K. Wang, A graph-theoretic approach to stability of neutral stochastic coupled oscillators network with time-varying delayed coupling, Math. Meth. Appl. Sci., 37 (2014), 1179-1190.
doi: 10.1002/mma.2879. |
[23] |
W. Li, H. Su, D. Wei and K. Wang, Global stability of coupled nonlinear systems with Markovian switching, Commun. Nonlinear Sci. Numer. Simulat., 17 (2012), 2609-2616.
doi: 10.1016/j.cnsns.2011.09.039. |
[24] |
C. Zhang, W. Li and K. Wang, Graph-theoretic approach to stability of multi-group models with dispersal, Discrete. Cont. Dyn-B., 20 (2015), 259-280.
doi: 10.3934/dcdsb.2015.20.259. |
[25] |
D. B. West, Introduction to Graph Theory, Prentice Hall, Upper Saddle River, 1996. |
[26] |
R. E. Mickens, Nonstandard finite difference schemes for differential equations, J. Differ. Equ. Appl., 8 (2002), 823-847.
doi: 10.1080/1023619021000000807. |
[27] |
S. M. Moghadas, M. E. Alexander and B. D. Corbett, A non-standard numerical scheme for a generalized Gause-type predator-prey model, Physica D., 188 (2004), 134-151.
doi: 10.1016/S0167-2789(03)00285-9. |
show all references
References:
[1] |
J. Wang, J. Zu, X. Liu, G. Huang and J. Zhang, Global dynamics of a multi-group epidemic model with general relapse distribution and nonlinear incidence rate, J. Biol. Syst., 20 (2012), 235-258.
doi: 10.1142/S021833901250009X. |
[2] |
H. Shu, D. Fan and J. Wei, Global stability of multi-group SEIR epidemic models with distributed delays and nonlinear transmission, Nonlinear Anal. RWA, 13 (2012), 1581-1592.
doi: 10.1016/j.nonrwa.2011.11.016. |
[3] |
C. Ji, D. Jiang, Q. Yang and N. Shi, Dynamics of a multigroup SIR epidemic model with stochastic perturbation, Automatica, 48 (2012), 121-131.
doi: 10.1016/j.automatica.2011.09.044. |
[4] |
H. Chen and J. Sun, Global stability of delay multigroup epidemic models with group mixing and nonlinear incidence rates, Appl. Math. Comput., 218 (2011), 4391-4400.
doi: 10.1016/j.amc.2011.10.015. |
[5] |
R. Sun and J. Shi, Global stability of multigroup epidemic model with group mixing and nonlinear incidence rates, Appl. Math. Comput., 218 (2011), 280-286.
doi: 10.1016/j.amc.2011.05.056. |
[6] |
M. Y. Li, Z. Shuai and C. Wang, Global stability of multi-group epidemic models with distributed delays, J. Math. Anal. Appl., 361 (2010), 38-47.
doi: 10.1016/j.jmaa.2009.09.017. |
[7] |
Y. Muroya, Y. Enatsu and T. Kuniya, Global stability for a multi-group SIRS epidemic model with varying population sizes, Nonlinear Anal. RWA, 14 (2013), 1693-1704.
doi: 10.1016/j.nonrwa.2012.11.005. |
[8] |
J. Epperlein, S. Siegmund and P. Stehík, Evolutionary games on graphs and discrete dynamical systems, J. Difference Eq. Appl., 21 (2015), 72-95.
doi: 10.1080/10236198.2014.988618. |
[9] |
M. Y. Li and Z. Shuai, Global-stability problem for coupled systems of differential equations on networks, J. Differ. Equ., 248 (2010), 1-20.
doi: 10.1016/j.jde.2009.09.003. |
[10] |
S. Elaydi, An Introduction to Difference Equations, 3rd ed, (Springer, New York, 2004). |
[11] |
G. Barlev, M. Girvan and E. Ott, Map model for synchronization of systems of many coupled oscillators, Chaos, 20 (2010), 023109.
doi: 10.1063/1.3357983. |
[12] |
M. Lazar, W. P. M. H. Heemels and A. R. Teel, Lyapunov functions, stability and input-to-state stability subtleties for discrete-time discontinuous systems, IEEE Trans. Autom. Control., 54 (2009), 2421-2425.
doi: 10.1109/TAC.2009.2029297. |
[13] |
J. Q. Qiu, K. F. Lu, P. Shi and M. S. Mahmoud, Robust exponential stability for discrete-time interval BAM neural networks with delays and Markovian jump parameters, Int. J. Adapt. Control., 24 (2010), 760-785.
doi: 10.1002/acs.1171. |
[14] |
M. S. Peng and X. Z. Yang, New stability criteria and bifurcation analysis for nonlinear discrete-time coupled loops with multiple delays, Chaos, 20 (2010), 013125, 11pp.
doi: 10.1063/1.3339857. |
[15] |
S. V. Naghavi and A. A. Safavi, Novel synchronization of discrete-time chaotic systems using neural network observer, Chaos, 18 (2008), 033110, 9pp.
doi: 10.1063/1.2959140. |
[16] |
J. D. Cao and J. Q. Lu, Adaptive synchronization of neural networks with or without time-varying delay, Chaos, 16 (2006), 013133, 6pp.
doi: 10.1063/1.2178448. |
[17] |
H. Su, W. Li and K. Wang, Global stability of discrete-time coupled systems on networks and its applications, Chaos, 22 (2012), 033135, 11pp.
doi: 10.1063/1.4748851. |
[18] |
C. Zhang, W. Li and K. Wang, Graph theory-based approach for stability analysis of stochastic coupled systems with Lévy noise on networks, IEEE Trans. Neural Netw. Learn. Syst., 26 (2014), 1698-1709.
doi: 10.1109/TNNLS.2014.2352217. |
[19] |
F. M. Atay and $\ddot Q$. Karabacak, Stability of coupled map networks with delays, SIAM J. Appl. Dyn. Syst., 5 (2006), 508-527.
doi: 10.1137/060652531. |
[20] |
H. Guo, M. L. Li and Z.Shuai, A graph-theoretic approach to the method of global Lyapunov functions, Proc. Amer. Math. Soc., 136 (2008), 2793-2802.
doi: 10.1090/S0002-9939-08-09341-6. |
[21] |
C. Zhang, W. Li and K. Wang, Boundedness for network of stochastic coupled van der Pol oscillators with time-varying delayed coupling, Appl. Math. Model., 37 (2013), 5394-5402.
doi: 10.1016/j.apm.2012.10.032. |
[22] |
C. Zhang, W. Li and K. Wang, A graph-theoretic approach to stability of neutral stochastic coupled oscillators network with time-varying delayed coupling, Math. Meth. Appl. Sci., 37 (2014), 1179-1190.
doi: 10.1002/mma.2879. |
[23] |
W. Li, H. Su, D. Wei and K. Wang, Global stability of coupled nonlinear systems with Markovian switching, Commun. Nonlinear Sci. Numer. Simulat., 17 (2012), 2609-2616.
doi: 10.1016/j.cnsns.2011.09.039. |
[24] |
C. Zhang, W. Li and K. Wang, Graph-theoretic approach to stability of multi-group models with dispersal, Discrete. Cont. Dyn-B., 20 (2015), 259-280.
doi: 10.3934/dcdsb.2015.20.259. |
[25] |
D. B. West, Introduction to Graph Theory, Prentice Hall, Upper Saddle River, 1996. |
[26] |
R. E. Mickens, Nonstandard finite difference schemes for differential equations, J. Differ. Equ. Appl., 8 (2002), 823-847.
doi: 10.1080/1023619021000000807. |
[27] |
S. M. Moghadas, M. E. Alexander and B. D. Corbett, A non-standard numerical scheme for a generalized Gause-type predator-prey model, Physica D., 188 (2004), 134-151.
doi: 10.1016/S0167-2789(03)00285-9. |
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