Free Access
Issue
Math. Model. Nat. Phenom.
Volume 11, Number 4, 2016
Ecology, Epidemiology and Evolution
Page(s) 73 - 88
DOI https://doi.org/10.1051/mmnp/201611406
Published online 19 July 2016
  1. H.D.I. Abarbanel, D. Creveling, R. Farisian, M. Kostuk. Dynamical state and parameter estimation. SIAM J. Appl. Dyn. Sys., 8 (4) (2009), 1341–1381. [CrossRef] [Google Scholar]
  2. M.W. Adamson, A. Yu. Morozov. When can we trust our model predictions? Unearthing structural sensitivity in biological systems. Proc. R. Soc., A 469 (2149) (2013), 20120500. [Google Scholar]
  3. D. Alonso, F. Bartumeus, J. Catalan. Mutual interfeence between predators can give rise to turing spatial patterns. Ecology, 83 (1) (2002), 28–34. [CrossRef] [Google Scholar]
  4. L. Chen, B. Liua, Z. Tengb. Analysis of a predator-prey model with Holling II functional response concerning impulsive control strategy. J. Comp. Appl. Math., 193 (2006), 347–362. [CrossRef] [Google Scholar]
  5. G. Besancon. Remarks on nonlinear adaptive observer design. Syst. Contr. Lett., 41 (2000), 271–280. [CrossRef] [Google Scholar]
  6. D. Brewer, M. Barenco, R. Callard, M. Hubank, J. Stark. Fitting ordinary differential equations to short time course data. Phil. Trans. R. Soc. A, 366 (2008), 519–544. [CrossRef] [Google Scholar]
  7. J. Distefano, C. Cobelli. On parameter and structural identifiabiliy: Nonunique observability/reconstructibility for identifiable systems, other ambiguities, and new definitions. IEEE Trans. Automat. Cont., AC-25 (4) (1980), 830–833. [CrossRef] [Google Scholar]
  8. D. Fairhurst, I.Yu. Tyukin, H. Nijmeijer, C. van Leeuwen. Observers for canonic models of neural oscillators. Math. Model. Nat. Phen., 5 (2) (2010), 146–184. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  9. M. Farza, M. M'Saad, T. Maatoung, M. Kamoun. Adaptive observers for nonlinearly parameterized class of nonlinear systems. Automatica, 45 (2009), 2292–2299. [CrossRef] [MathSciNet] [Google Scholar]
  10. A.N. Gorban. Slow relaxations and bifurcations of omega-limit sets of dynamical systems. PhD thesis, Kuibyshev, Russia, 1980. [Google Scholar]
  11. A.N. Gorban. Singularities of transition processes in dynamical systems: Qualitative theory of critical delays electron. Electr. J. Diff. Eqns., Monograph 5 (2004). http://ejde.math.txstate.edu/Monographs/05/. [Google Scholar]
  12. H.F. Grip, T.A. Johansen, L. Imsland, G.O. Kaasa. Parameter estimation and compensation in systems with nonlinearly parameterized perturbations. Automatica, 46 (1) (2010), 19–28. [CrossRef] [MathSciNet] [Google Scholar]
  13. A.L. Hodgkin, A.F. Huxley. A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol., 117 (1952), 500–544. [CrossRef] [PubMed] [Google Scholar]
  14. E. Izhikevich. Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting. MIT Press, 2007. [Google Scholar]
  15. T. Johnson, W. Tucker. Rigorous parameter reconstruction for differential equations with noisy data. Automatica, 44 (2008), 2422–2426. [CrossRef] [MathSciNet] [Google Scholar]
  16. P. Kuhl, M. Deihl, T. Kraus, J. P. Schloder, Bock H. G. A real-time algorithm for moving horizon state and parameter estimation. Comp. Chem. Eng., 35 (1) (2011), 71–83. [CrossRef] [Google Scholar]
  17. A. Loria, E. Panteley. Uniform exponential stability of linear time-varying systems: revisited. Syst. Contr. Lett., 47 (1) (2003), 13–24. [CrossRef] [Google Scholar]
  18. Z.J. Jing, L.S. Chen. The existence and uniqueness of limit cycles in general predator-prey differential equations. Chineese Sci. Bull., 9 (1984), 521–523. [Google Scholar]
  19. R. Marino, P. Tomei. Global adaptive observers for nonlinear systems via filtered transformations. IEEE Trans. Automat. Contr., 37 (8) (1992), 1239–1245. [CrossRef] [Google Scholar]
  20. H. Miao, X. Xia, A. Perelson, H. Wu. On identifiability of nonlinear ode models and applications in viral dynamics. SIAM Rev., 53 (1) (2011), 3–39. [CrossRef] [MathSciNet] [Google Scholar]
  21. C. Morris, H. Lecar. Voltage oscillations in the barnacle giant muscle fiber. Biophys. J., 35 (1981), 193–213. [CrossRef] [PubMed] [Google Scholar]
  22. J.A. Nelder, R. Mead. A simplex method for function minimization. Comp. J., 7 (1965), 308–313. [Google Scholar]
  23. A. Pavlov, B.G.B. Hunnekens, N.v.d. Wouw, H. Nijmeijer. Steady-state performance optimization for nonlinear control systems. Automatica, 49 (7) (2013), 2087–2097. [CrossRef] [MathSciNet] [Google Scholar]
  24. I. Tyukin. Adaptation in Dynamical Systems. Cambridge Univ. Press, 2011. [Google Scholar]
  25. I. Tyukin, E. Steur, H. Nijmeijer, C. van Leeuwen. Adaptive observers and parameter estimation for a class of systems nonlinear in the parameters. Automatica, 49 (8) (2013), 2409–2423. [CrossRef] [MathSciNet] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.