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Applicable Analysis
An International Journal
Volume 96, 2017 - Issue 6
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Articles

Exponential synchronization of stochastic coupled oscillators networks with delays

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Pages 1058-1075 | Received 18 Nov 2013, Accepted 11 Apr 2016, Published online: 04 May 2016

References

  • Zhang C, Zheng B, Wang L. Multiple Hopf bifurcations of three coupled van der Pol oscillators with delay. Appl. Math. Comput. 2011;217:7155–7166.
  • Hirano N, Rybicki S. Existence of limit cycles for coupled van der Pol equations. J. Differ. Equ. 2003;195:194–209.
  • Wu J, Jiao L, Li R, et al. Clustering dynamics of nonlinear oscillator network: application to graph coloring problem. Physica D. 2011;240:1972–1978.
  • Zhou J, Cheng X, Xiang L, et al. Impulsive control and synchronization of chaotic systems consisting of Van der Pol oscillators coupled to linear oscillators. Chaos Solitons Fractals. 2007;33:607–616.
  • Zhang J, Guo X. Stability and bifurcation analysis in the delay-coupled van der Pol oscillators. Appl. Math. Model. 2010;34:2291–2299.
  • Kim S, Park SH, Ryu CS. Multistability in coupled oscillator systems with time delay. Phys. Rev. Lett. 1997;79:2911–2914.
  • Choi MY, Kim HJ, Kim D, et al. Synchronization in a system of globally coupled oscillators with time delay. Phys. Rev. E. 2000;61:371–381.
  • Wang Y, Wang Z, Liang J, et al. Synchronization of stochastic genetic oscillator networks with time delays and Markovian jumping parameters. Neurocomputing. 2010;73:2532–2539.
  • Xiao Y, Tang S, Xu Y. Theoretical analysis of multiplicative-noise-induced complete synchronization in global coupled dynamical network. Chaos. 2012;22:013110.
  • Sun Y, Li W, Zhao D. Finite-time stochastic outer synchronization between two complex dynamical networks with different topologies. Chaos. 2012;22:023152.
  • Mori F, Odagaki T. Synchronization of coupled oscillators on small-world networks. Physica D. 2009;238:1180–1185.
  • Yang Y, Cao J. Exponential synchronization of the complex dynamical networks with a coupling delay and impulsive effects. Nonlinear Anal. RWA. 2010;11:1650–1659.
  • Ji DH, Jeong SC, Park JH, et al. Adaptive lag synchronization for uncertain complex dynamical network with delayed coupling. Appl. Math. Comput. 2012;218:4872–4880.
  • Ma J, Li F, Huang L, et al. Complete synchronization, phase synchronization and parameters estimation in a realistic chaotic system. Commun. Nonlinear Sci. Numer. Simul. 2011;16:3770–3785.
  • Zhu Q, Cao J. {\it p}th moment exponential synchronization for stochastic delayed Cohen--Grossberg neural networks with Markovian switching. Nonlinear Dyn. 2012;67:829–845.
  • Hu C, Yu J, Jiang H, et al. Exponential synchronization for reaction--diffusion networks with mixed delays in terms of p-norm via intermittent driving. Neural Netw. 2012;31:1–11.
  • Wang L, Qian W, Wang Q. Exponential synchronization in complex networks with a single coupling delay. J. Frankl. Inst.-Eng. Appl. Math. 2013;350:1406–1423.
  • Lin W, He Y. Complete synchronization of the noise-perturbed Chuas circuits. Chaos. 2005;15:023705.
  • Liu Y, Wang Z, Liu X. Exponential synchronization of complex networks with Markovian jump and mixed delays. Phys. Lett. A. 2008;372:3986–3998.
  • Njah AN, Vincent UE. Chaos synchronization between single and double wells Duffing--Van der Pol oscillators using active control. Chaos Solitons Fractals. 2008;37:1356–1361.
  • Sun Y, Cao J. Adaptive synchronization between two different noise-perturbed chaotic systems with fully unknown parameters. Physica A. 2007;376:253–265.
  • Wu Z, Chen G, Fu X. Synchronization of a network coupled with complex-variable chaotic systems. Chaos. 2012;22:023127.
  • Guo H, Li MY, Shuai Z. A graph-theoretic approach to the method of global Lyapunov functions. Proc. Amer. Math. Soc. 2008;136:2793–2802.
  • Li MY, Shuai Z. Global-stability problem for coupled systems of differential equations on networks. J. Differ. Equ. 2010;248:1–20.
  • Guo H, Li MY, Shuai Z. Global dynamics of a general class of multistage models for infectious diseases. SIAM J. Appl. Math. 2012;72:261–279.
  • Li W, Su H, Wang K. Global stability analysis for stochastic coupled systems on networks. Automatica. 2011;47:215–220.
  • Li W, Su H, Wei D, et al. Global stability of coupled nonlinear systems with Markovian switching. Commun. Nonlinear Sci. Numer. Simul. 2012;17:2609–2616.
  • Li W, Song H, Qu Y, et al. Global exponential stability for stochastic coupled systems on networks with Markovian switching. Syst. Control Lett. 2013;62:468–474.
  • 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.
  • 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.
  • Yang Q, Mao X. Extinction and recurrence of multi-group SEIR epidemic models with stochastic perturbations. Nonlinear Anal. RWA. 2013;14:1434–1456.
  • Ji C, Jiang D, Shi N. Multigroup SIR epidemic model with stochastic perturbation. Physica A. 2011;390:1747–1762.
  • Li MY, Shuai Z, Wang C. Global stability of multi-group epidemic models with distributed delays. J. Math. Anal. Appl. 2010;361:38–47.
  • Shu H, Fan D, Wei J. Global stability of multi-group SEIR epidemic models with distributed delays and nonlinear transmission. Nonlinear Anal. RWA. 2012;13:1581–1592.
  • Chen H, Sun J. Stability analysis for coupled systems with time delay on networks. Physica A. 2012;391:528–534.
  • Zhang C, Li W, Wang K. A graph-theoretic approach to stability of neutral stochastic coupled oscillators network with time-varying delayed coupling. Math. Meth. Appl. Sci. 2014;37:1179–1190.
  • Li W, Pang L, Su H, et al. Global stability for discrete Cohen--Grossberg neural networks with finite and infinite delays. Appl. Math. Lett. 2012;25:2246–2251.
  • Su H, Li W, Wang K. Global stability analysis of discrete-time coupled systems on networks and its applications. Chaos. 2012;22:033135.
  • Suo J, Sun J, Zhang Y. Stability analysis for impulsive coupled systems on networks. Neurocomputing. 2013;99:172–177.
  • West DB. Introduction to graph theory. Upper Saddle River (NJ): Prentice Hall; 1996.
  • Santos AM, Lopes SR, Viana RL. Rhythm synchronization and chaotic modulation of coupled Van der Pol oscillators in a model for the heartbeat. Physica A. 2004;338:335–355.
  • Marra AM, Mannini C, Bartoli G. Van der Pol-type equation for modeling vortex-induced oscillations of bridge decks. J. Wind Eng. Ind. Aerodyn. 2011;99:776–785.
  • Mao X, Yuan C. Stochastic differential equations with Markovian switching. London: Imperial College Press; 2006.
  • Mao X. Stochastic differential equations and their applications. Chichester: Horwood Publishing; 1997.
  • Su H, Qu Y, Gao S, et al. A model of feedback control system on network and its stability analysis. Commun. Nonlinear Sci. Numer. Simul. 2013;18:1822–1831.
  • Bao J, Mao X, Yin G, et al. Competitive Lotka-Volterra population dynamics with jumps. Nonlinear Anal. 2011;74:6601–6616.
  • Liu Z, Lü S, Zhong S, et al. {it p}th moment exponential synchronization analysis for a class of stochastic neural networks with mixed delays. Commun. Nonlinear Sci. Numer. Simulat. 2010;15:1899–1909.

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