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Applicable Analysis
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Volume 96, 2017 - Issue 12
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Articles

Periodic solutions for neutral coupled oscillators network with feedback and time-varying delay

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Pages 1983-2001 | Received 06 Jan 2016, Accepted 07 Jun 2016, Published online: 24 Jun 2016

References

  • Mackay RS, Aubry S. Proof of existence of breathers for time-reversble or hamiltonion networks of weakly coupled oscillators. Nonlinearity. 1994;7:1623–1643.
  • Ashwin P, Timme M. Unstable attractors: existence and robustness in networks of oscillators with delayed pulse coupling. Nonlinearity. 2005;18:2035–2060.
  • Panaggio MJ, Abrams DM. Chimera states: coexistence of coherence and incoherence in networks of coupled oscillators. Nonlinearity. 2015;28:R67–R87.
  • Niu B, Guo YX, Wang HB. Multiple bifurcation analysis in a ring of delay coupled oscillators with neutral feedback. Nonlinear Dynamics. 2013;73:1475–1492.
  • Guo YX, Niu B. Amplitude death and spatiotemporal bifurcations in nonlocally delay-coupled oscillators. Nonlinearity. 2015;28:1841–1858.
  • Aon MA, Cortassa S, Brian OR. The fundamental organization of cardiac mitochondria as a network of coupled oscillators. Biophys. J. 2006;91:4317–4327.
  • Egelhaaf M, Benjamin PR. Coupled neuronal oscillators in the snail Lymnaea stagnalis: endogenous cellular properties and network interactions. J. Exp. Biology. 2009;80:066213.
  • Su HS, Wang XF. Lin. ZL. Synchronization of coupled harmonic oscillators in a dynamic proximity network. Automatica. 2009;45:2286–2291.
  • Roychowdhury J, Bhushan P. Hierarchical abstraction of weakly coupled synchronized oscillator networks. Int. J. Numer. Methods Eng. 2015;102:1041–1076.
  • Orlando DA, Lin CY, Bernard A. Global control of cell-cycle transcription by coupled CDK and network oscillators. Nature. 2008;453:944–U78.
  • Bristow SL, Leman AR, Kovacs LA. Checkpoints couple transcription network oscillator dynamics to cell-cycle progression. Genome Biology. 2014;15:446.
  • Zhang CM, Li WX, 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 CM, Li WX, 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.
  • Li CG, Xu HB, Liao XF. Synchronization in small-world oscillator networks with coupling delays. Physica A. 2004;335:359–364.
  • Kyrychko YN, Blyuss KB. Schoell. E. Synchronization of networks of oscillators with distributed delay coupling. Chaos. 2014;24:043117.
  • Funato T, Kurabayashi D. Network structure for control of coupled multiple nonlinear oscillators. IEEE Trans. Syst. Man Cybern. Part B Cybern. 2008;38:675–681.
  • Kerckhoff J, Andrews RW, Ku HS. Tunable coupling to a mechanical oscillator circuit using a coherent feedback network. Phys. Rev. X. 2013;3:021013.
  • Wei JJ, Jiang WH. Stability and bifurcation analysis in Van der Pol’s oscillator with delayed feedback. J. Sound Vibr. 2005;283:801–819.
  • Zhou Y, Jiao F, Li J. Existence and uniqueness for fractional neutral differential equations with infinite delay. Nonlinear Anal. Theory Methods Appl. 2009;71:3249–3256.
  • Xu SY, Lam J, Ho DWC. Delay-dependent exponential stability for a class of neural networks with time delays. J. Comput. Appl. Math. 2005;183:16–28.
  • Sepulchre JA, MacKay RS. Localized oscillations in conservative or dissipative networks of weakly coupled autonomous oscillators. Nonlinearity. 1997;10:679–713.
  • Bambusi D. Exponential stability of breathers in Hamiltonian networks of weakly coupled oscillators. Nonlinearity. 1996;9:433–457.
  • Balanov Z, Krawcewicz W. Rachinskii. D. Hopf bifurcation in symmetric networks of coupled oscillators with hysteresis. J. Dyn Differ. Equ. 2012;24:713–759.
  • Bambusi D. Asymptotic stability of breathers in some hamiltonian networks of weakly coupled oscillators. Commun. Math. Phys. 2013;324:515–547.
  • Li YK, Kuang Y. Periodic solutions of periodic delay Lotka-Volterra equations and systems. J. Math. Anal. Appl. 2001;255:260–280.
  • Bohner M, Fan M, Zhang JM. Existence of periodic solutions in predator-prey and competition dynamic systems. Nonlinear Anal. Real World Appl. 2006;7:1193–1204.
  • Zeng GZ, Wang FY, Nieto JJ. Complexity of a delayed predator-prey model with impulsive harvest and holling type II functional response. Adv. Complex. 2008;11:77–97.
  • Guo SJ, Huang LH. Periodic oscillation for discrete-time Hopfield neural networks. Phys. Lett. A. 2004;329:199–206.
  • Guo HB, Li MY, Shuai ZS. A graph-theoretic approach to the method of global Lyapunov functions. Proc. Am. Math. Soc. 2008;136:2793–2802.
  • Li MY, Shuai ZS. Global-stability problem for coupled systems of differential equations on networks. J. Differ. Equ. 2010;248:1–20.
  • Li WX, Chen TR, Xu DG. Synchronization of delayed coupled reaction-diffusion systems on networks. Math. Methods Appl. Sci. 2015;38:2216–2228.
  • Li WX, Su H, Wei DG. Global stability of coupled nonlinear systems with Markovian switching. Commun. Nonlinear Sci. Numer. Simul. 2012;17:2609–2616.
  • Su H, Li WX, Wang K. Global stability analysis of discrete-time coupled systems on networks and its applications. Chaos. 2012;22:033135.
  • Li WX, Pang LS, Su H. Global stability for discrete Cohen-Grossberg neural networks with finite and infinite delays. Appl. Math. Lett. 2012;25:2246–2251.
  • Earl MG, Strogatz SH. Synchronization in oscillator networks with delayed coupling: A stability criterion. Phys. Rev. E. 2003;67:036204.
  • Porfiri M, Bernardo M. Criteria for global pinning-controllability of complex networks. Automatica. 2008;44:3100–3106.
  • Harary F. Graph theory. Reading (MA): Addison-Wesley; 1969.
  • West DB. Introduction to Graph theory. Upper Saddle River: Prentice Hall; 1996.
  • Gaines R, Mawhin J. Coincidence degree and nonlear differential equations. Berlin: Springer; 1977.
  • Su WW, Chen YM. Global asymptotic stability analysis for neutral stochastic neural networks with time-varying delays. Commun. Nonlinear Sci. Numer. Simul. 2009;14:1576–1581.
  • Luo Q, Mao XR, Shen Y. New criteria on exponential stability of neutral stochastic differential delay equations. Syst. Control Lett. 2006;55:826–834.

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