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Articles

Practical dynamic consensus of Stuart–Landau oscillators over heterogeneous networks

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Pages 261-273 | Received 10 Mar 2018, Accepted 11 Oct 2018, Published online: 15 May 2019

References

  • Andronov, A. A., Vitt, A. A., & Khakin, S. E. (1987). Theory of oscillators. New York: Dover Mathematics. Original in Russian, 1959.
  • Angeli D., & Efimov D. (2013). On input-to-state stability with respect to decomposable invariant sets. Proceedings of the 52nd IEEE conference on decision and control (pp. 5897–5902). Florence.
  • Aoyagi T. (1995). Network of neural oscillators for retrieving phase information. Physical Review Letters, 74, 4075–4078. doi: 10.1103/PhysRevLett.74.4075
  • Belhaq M., & Houssni M. (2000). Suppression of chaos in averaged oscillator driven by external and parametric excitations. Chaos, Solitons and Fractals, 11(8), 1237–1246. doi: 10.1016/S0960-0779(98)00334-8
  • Bergner A., Frasca M., Sciuto G., Buscarino A., Ngamga E. J., Fortuna L., & Kurths J. (2012, February). Remote synchronization in star networks. Physical Review E, 85, 026208. doi:10.1103/PhysRevE.85.026208
  • Cagnan H., Meijer H. G., Gils S. A., Krupa M., Heida T., Rudolph M., & H. C. Martens (2009). Frequency-selectivity of a thalamocortical relay neuron during Parkinson's disease and deep brain stimulation : A computational study. European Journal of Neuroscience, 30(7), 1306–1317. doi: 10.1111/j.1460-9568.2009.06922.x
  • Carr T., Taylor M., & Schwartz I. (2006). Negative-coupling resonances in pump-coupled lasers. Physica D: Nonlinear Phenomena, 213(2), 152–163. doi: 10.1016/j.physd.2005.10.015
  • Corless M., & Leitmann G. (1981). Continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems. IEEE Transaction on Automatic Control, 26(5), 1139–1144. doi: 10.1109/TAC.1981.1102785
  • Craven B. D. (1969). Complex symmetric matrices. Journal of the Australian Mathematical Society, 10, 341–354. doi: 10.1017/S1446788700007588
  • Dunn J. M., & Anderssen R. S. (2011). A review of models used for understanding epileptic seizures. In International Congress on Modelling and Simulation. Perth.
  • Franci A., Chaillet A., Panteley E., & Lamnabhi-Lagarrigue F. (2012). Desynchronization and inhibition of Kuramoto oscillators by scalar mean-field feedback. Mathematics of Control, Signals and Systems, 24(1-2), 169–217. doi: 10.1007/s00498-011-0072-9
  • Franci A., Scardovi L., & Chaillet A. (2011). An input-output approach to the robust synchronization of dynamical systems with an application to the Hindmarsh-Rose neuronal model. In Proc. of the joint IEEE conference on decision and control and european control conference, Orlando, FL, USA (pp. 6504–6509).
  • Horn, R. A., & Johnson, C. R. (1985). Matrix analysis. Cambridge: Cambridge Press.
  • Ipsen M., Hynne F., & Soerensen P. G. (1997, November). Amplitude equations and chemical reaction-diffusion systems. International Journal of Bifurcation and Chaos, 7(7), 1539–1554. doi: 10.1142/S0218127497001217
  • Jouffroy J., & Slotine J. J. (2004). Methodological remarks on contraction theory. In Proceedings of the 43rd IEEE conference on decision and control, Nassau, Bahamas (Vol. 3, pp. 2537–2543).
  • Karnatak R., Ramaswamy R., & Prasad A. (2007). Amplitude death in the absence of time delays in identical coupled oscillators. Physical Review E, 76, 035201. doi: 10.1103/PhysRevE.76.035201
  • Khalil, H. (2002). Nonlinear systems (3rd ed). Upper Saddle River, NJ: Prentice Hall.
  • Kuramoto Y. (1975). Self-entrainment of a population of coupled non-linear oscillators. Lecture Notes in Physics, 39, 420–422. doi: 10.1007/BFb0013365
  • Kuznetsov, Y. A. (1998). Elements of applied bifurcation theory (Vol. 112). New York: Springer.
  • Lehnert J., Hövel P., Selivanov A., Fradkov A. L., & Schöll E. (2014). Controlling cluster synchronization by adapting the topology. Physical Review E, 90(4), 042914. doi: 10.1103/PhysRevE.90.042914
  • Lohmiller W., & Slotine J. J. (2005). Contraction analysis of non-linear distributed systems. International Journal of Control, 78, 678–688. doi: 10.1080/00207170500130952
  • Mallet N., Pogosyan A., Marton F., Bolam J. P., Brown P., & Magill P. J. (2008). Parkinsonian beta oscillations in the external globus Pallidus and their relationship with Subthalamic Nucleus activity. Journal of Neuroscience, 28(7), 14245–14258. doi: 10.1523/JNEUROSCI.4199-08.2008
  • Matthews P. C., Mirollo R. E., & Strogatz S. H. (1991). Dynamics of a large system of coupled nonlinear oscillators. Physica D: Nonlinear Phenomena, 52, 293–331. doi: 10.1016/0167-2789(91)90129-W
  • Mormann F., Lehnertz K., David P., & Elger C. E. (2000). Mean phase coherence as a measure for phase synchronization and its application to the eeg of epilepsy patients. Physica D: Nonlinear Phenomena, 144(4), 358–369. doi: 10.1016/S0167-2789(00)00087-7
  • Moro J., Burke J., & Overton M. (1997). On the Lidskii-Vishik-Lyusternik perturbation theory for eigenvalues of matrices with arbitrary Jordan structure. SIAM Journal on Matrix Analysis and Applications, 18(4), 793–817. doi: 10.1137/S0895479895294666
  • Olfati-Saber R., & Murray R. (2004). Consensus problems in networks of agents with switching topology and time-delays. Automatic Control, IEEE Transactions on, 49(9), 1520–1533. doi: 10.1109/TAC.2004.834113
  • Panteley E., Loría A., & El Ati A. (2015). Analysis and control of andronov-hopf oscillators with applications to neuronal populations. In Proc. 54th IEEE Conf. Decision and Control (pp. 596–601). Osaka. doi:10.1109/CDC.2015.7402294
  • Panteley E., Loría A., & El Ati A. (2015). On the stability and robustness of Stuart-Landau oscillators. in Proc. 1st IFAC Conference onModelling, Identification andControl of Nonlinear Systems, MICNON 2015, (St. Petersburg, Russia). IFAC-PapersOnLine, 48(1), 645–650. doi:10.1016/j.ifacol.2015.09.260
  • Panteley E., & Loria A. (2017). Synchronization and dynamic consensus of heterogeneous networked systems. IEEE Transactions on Automatic Control, 62(8), 3758–3773. Pre-published online. doi:10.1109/TAC.2017.2649382
  • Perko, L. (2000). Differential equations and dynamical systems. New York: Springer.
  • Pham Q. C., & Slotine J. J. (2007). Stable concurrent synchronization in dynamic system networks. Neural Networks, 20(1), 62–77. doi: 10.1016/j.neunet.2006.07.008
  • Pogromsky A. Y., Glad T., & Nijmeijer H. (1999). On difffusion driven oscillations in coupled dynamical systems. International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 9(4), 629–644. doi: 10.1142/S0218127499000444
  • Pogromsky A. Y., & Nijmeijer H. (2001). Cooperative oscillatory behavior of mutually coupled dynamical systems. IEEE Transaction on Circuits and Systems I: Fundamental Theory and Applications, 48(2), 152–162. doi: 10.1109/81.904879
  • Qin Y. M., Men C., Zhao J., Han C. X., & Che Y. Q. (2018). Toward heterogeneity in feedforward network with synaptic delays based on fitzhughnagumo model. International Journal of Modern Physics B, 32(1), 1750274. doi:10.1142/S0217979217502745
  • Ren W., Beard R., & Atkins E. (2007, April). Information consensus in multivehicle cooperative control. Control Systems, IEEE, 27(2), 71–82. doi:10.1109/MCS.2007.338264
  • Rosenblum M. G., & Pikovsky A. S. (2004). Controlling synchronization in an ensemble of globally coupled oscillators. Physical Review Letters, 92(1), 114102.
  • Sakaguchi H., & Kuramoto Y. (1986). A soluble active rotater model showing phase transitions via mutual entertainment. Progress of Theoretical Physics, 76(3), 576–581. doi: 10.1143/PTP.76.576
  • Scardovi L., Arcak M., & Sontag E. D. (2009). Synchronization of interconnected systems with an input-output approach. Part I: Main results. In Proceedings of the 48th IEEE conference on decision and control, Atlanta, GA, USA (pp. 609–614).
  • Selivanov A., Lehnert J., Dahms T., Hövel P., Fradkov A. L., & Schöll E. (2012, January). Adaptive synchronization in delay-coupled networks of Stuart-Landau oscillators. Physical Review E, 85, 016201. doi: 10.1103/PhysRevE.85.016201
  • Steur E., Tyukin I., Gorban A., Jarman N., Nijmeijer H., & van Leeuwen C. (2016). Coupling-modulated multi-stability and coherent dynamics in directed networks of heterogeneous nonlinear oscillators with modular topology. IFAC-PapersOnLine, 49(4), 62–67. 6th IFAC Workshop on Periodic Control Systems PSYCO 2016. doi: 10.1016/j.ifacol.2016.07.981
  • Strogatz S. H. (2000). From kuramoto to crawford: Exploring the onset of synchronization in populations of coupled oscillators. Physica D: Nonlinear Phenomena, 143(14), 1–20. doi: 10.1016/S0167-2789(00)00094-4
  • Sune D. (2005). Chemical interpretation of oscillatory modes at a Hopf point. Physical Chemistry Chemical Physics, 7, 1674–1679. doi: 10.1039/B415437A
  • Teel A. R., Peuteman J., & Aeyels D. (1999). Semi-global practical asymptotic stability and averaging. Systems and Control Letters, 37(5), 329–334. doi: 10.1016/S0167-6911(99)00039-0
  • Teramae J. N., & Tanaka D. (2004). Robustness of the noise-induced phase synchronization in a general class of limit cycle oscillators. Physical Review Letters, 93, 204103. doi: 10.1103/PhysRevLett.93.204103
  • Wang L., Chen M. Z., & Wang Q. G. (2015). Bounded synchronization of a heterogeneous complex switched network. Automatica, 56, 19–24. doi: 10.1016/j.automatica.2015.03.020
  • Wilkinson, J. H. (1965). The algebraic eigenvalue problem (Vol. 87). Oxford: Clarendon Press Oxford.
  • Zhang F., Trentelman H. L., & Scherpen J. M. A. (2016). Robust cooperative output regulation of heterogeneous lur'e networks. International Journal of Robust and Nonlinear Control, 27(6), 3061–3078. doi:10.1002/rnc.3725

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