Geodesic
Computation of inertial manifolds in biological models. FitzHugh–Nagumo model
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2007), pp. 102-111 
Cristina Nartea. Computation of inertial manifolds in biological models. FitzHugh–Nagumo model. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2007), pp. 102-111. http://geodesic.mathdoc.fr/item/BASM_2007_3_a8/
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     title = {Computation of inertial manifolds in biological models. {FitzHugh{\textendash}Nagumo} model},
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Voir la notice de l'article provenant de la source Math-Net.Ru

Inertial manifolds are related to the large time behaviour of dynamical systems. An algorithm, based on the Lyapunov–Perron method, is implemented here and used to construct a sequence of approximate inertial manifolds for a biological model. The hypotheses of the Jolly, Rosa, Temam's algorithm are verified for the FitzHugh–Nagumo model in the case of real eigenvalues. This algorithm is used for the construction of approximate inertial manifolds.

[1] FitzHugh R., “Impulses and physiological states in theoretical models of nerve membrane”, Biophysical J., 1 (1961), 445–446 | DOI

[2] Georgescu A., Rocoreanu C., Giurgieanu N., “Global bifurcations in FitzHugh-Nagumo model”, Trends in Mathematics: Bifurcations, Symmetry and Patterns, Birkhäuser Verlag, Basel, Switzerland, 2003, 197–202 | MR | Zbl

[3] Rocoreanu C., Georgescu A., Giurgieanu N., The FitzHugh-Nagumo model. Bifurcation and Dynamics, Kluwer, Dordrecht, 2000 | MR

[4] Jolly M. S., Rosa R., “Computation of non-smooth local centre manifolds”, IMA J. of Numerical Analysis, 25 (2005), 698–725 | DOI | MR | Zbl

[5] Jolly M. S., Rosa R., Temam R., “Accurate computations on inertial manifold”, SIAM J. Sci. Comput., 22:6 (2000), 2216–2238 | DOI | MR

[6] Rosa R., “Approximate inertial manifolds of exponential order”, Discrete and Continuous Dynamical Systems, 1 (1995), 421–448 | DOI | MR | Zbl

[7] Rosa R., Temam R., “Inertial manifolds and normal hyperbolicity”, ACTA Applicandae Mathematicae, 45 (1996), 1–50 | DOI | MR | Zbl

[8] Temam R., Infinite-dimensional dynamical systems in mechanics and physics, Applied Mathematical Sciences, 68, Springer, Berlin, 1997 | MR | Zbl

[9] Tu P., Dynamical systems. An introduction with applications in economics and biology, Springer, Berlin, 1994 | MR

[10] www.scilab.org/