305
Views
23
CrossRef citations to date
0
Altmetric
Original Articles

Optimal control of stochastic FitzHugh–Nagumo equation

, &
Pages 746-756 | Received 18 Apr 2015, Accepted 13 Sep 2015, Published online: 04 Nov 2015

References

  • Albeverio, S., & Di Persio, L. (2011). Some stochastic dynamical models in neurobiology: Recent developments. Europena Communications in Mathematical and Theoretical Biology, 14, 44–53.
  • Barbu, V. (2010). Nonlinear differential equations of monotone types in Banach spaces. New York, NY: Springer.
  • Barbu, V., & Iannelli, M. (1999). Optimal control of population dynamics. Journal of Optimization Theory and Applications, 102(1), 1–14.
  • Barbu, V., & Precupanu, T. (2012). Convexity and optimization in Banach spaces. Dordrecht: D. Reidel Publishing Company.
  • Barbu, V., & Röckner, M. (2011). On a random scaled porous media equation. Journal of Differential Equations, 251(9), 2494–2514.
  • Bonaccorsi, S., Marinelli, C., & Ziglio, G. (2008). Stochastic FitzHugh-Nagumo equations on networks with impulsive noise. Electronic Journal of Probability, 13, 1362–1379.
  • Casas, E., Ryll, C., & Tröltzsch, F. (2013). Sparse optimal control of the Schlögl and FitzHugh–Nagumo systems. Computational Methods in Applied Mathematics, 13(4), 415–442.
  • Da Prato, G. (2004). Kolmogorov equations for stochastic PDEs. Advanced Courses in Mathematics. Basel: Birkhäuser Verlag.
  • Da Prato, G., & Zabczyk, J. (1996). Ergodicity for infinite-dimensional systems. Cambridge: Cambridge University Press.
  • Diehl, H.W. (1997). The theory of boundary critical phenomena. International Journal of Modern Physics B, 11(30), 3503–3523.
  • Ekeland, I. (1974). On the variational principle. Journal of Mathematical Analysis and Applications, 47(2), 324–353.
  • FitzHugh, R. (1961). Impulses and physiological states in theoretical models of nerve membrane. Biophysical Journal, 1, 445–466.
  • Fuhrman, M., & Tessitore, G. (2002). Nonlinear Kolmogorov equations in infinite dimensional spaces: The backward stochastic differential equations approach and applications to optimal control. Annals of Probability, 3:1397–1465.
  • Kunisch, K., & Wagner, M. (2013). Optimal control of the bidomain system (III): Existence of minimizers and first-order optimality conditions. ESAIM: Mathematical Modelling and Numerical Analysis, 47(04), 1077–1106.
  • Nagumo, J., Arimoto, S., & Yoshizawa, S. (1962). An active pulse transmission line simulating nerve axon. Proceedings of the Institute of Radio Engineers, 50(10), 2061–2070.
  • Pitchaiah, S., & Armaou, A. (2010). Output feedback control of the FitzHugh-Nagumo equation using adaptive model reduction. In Proceedings of the 49th IEEE Conference on Decision and Control (pp. 864–869). Atlanta, GA. New York, NY: Institute of Electrical and Electronics Engineers (IEEE).
  • Tessitore, G. (1996). Existence, uniqueness and space regularity of the adapted solutions of a backward SPDE. Stochastic Analysis and Applications, 14(4), 461–486.
  • Tuckwell, H.C. (1992). Random perturbations of the reduced Fitzhugh-Nagumo equation. Physica Scripta, 46(6), 481–484.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.