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Título

Stabilization of inhomogeneous patterns in a diffusion-reaction system under structural and parametric uncertainties

AutorVilas Fernández, Carlos ; García, Miriam R. ; Banga, Julio R. ; Alonso, Antonio A.
Palabras claveNonlinear reaction–diffusion systems
Excitable medium
Robust nonlinear control
FitzHugh–Nagumo
Moving front stabilization
Limit cycles control
Reduced order models
Cardiac disorders
Neuron transmission
Fecha de publicación2006
EditorElsevier
CitaciónJournal of Theoretical Biology 241(2): 295-306 (2006)
ResumenMany phenomena such as neuron firing in the brain, the travelling waves which produce the heartbeat, arrythmia and fibrillation in the heart, catalytic reactions or cellular organization activities, among others, can be described by a unifying paradigm based on a class of nonlinear reaction–diffusion mechanisms. The FitzHugh–Nagumo (FHN) model is a simplified version of such class which is known to capture most of the qualitative dynamic features found in the spatiotemporal signals. In this paper, we take advantage of the dissipative nature of diffusion–reaction systems and results in finite dimensional nonlinear control theory to develop a class of nonlinear feedback controllers which is able to ensure stabilization of moving fronts for the FHN system, despite structural or parametric uncertainty. In the context of heart or neuron activity, this class of control laws is expected to prevent cardiac or neurological disorders connected with spatiotemporal wave disruptions. In the same way, biochemical or cellular organization related with certain functional aspects of life could also be influenced or controlled by the same feedback logic. The stability and robustness properties of the controller will be proved theoretically and illustrated on simulation experiments
Descripción12 páginas, 6 figuras, 1 tabla
Versión del editorhttp://dx.doi.org/10.1016/j.jtbi.2005.11.030
URIhttp://hdl.handle.net/10261/50835
DOI10.1016/j.jtbi.2005.11.030
ISSN0022-5193
E-ISSN1095-8541
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