Steady states of FitzHugh-Nagumo system with non-diffusive activator and diffusive inhibitor

• Verfasst von: Li, Ying [VerfasserIn]
• Verfasst von: Marciniak-Czochra, Anna [VerfasserIn]
• Verfasst von: Takagi, Izumi [VerfasserIn]
• Titel: Steady states of FitzHugh-Nagumo system with non-diffusive activator and diffusive inhibitor
• Verf.angabe: Ying Li, Anna Marciniak-Czochra, Izumi Takagi, and Boying Wu
• E-Jahr: 2019
• Jahr: 21 June 2019
• Umfang: 37 S.
• Fussnoten: Gesehen am 26.08.2019
• Titel Quelle: Enthalten in: Tōhoku mathematical journal
• Ort Quelle: Sendai : Univ., 1911
• Jahr Quelle: 2019
• Band/Heft Quelle: 71(2019), 2, Seite 243-279
• ISSN Quelle: 1881-2015
• DOI: doi:10.2748/tmj/1561082598
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: bifurcation analysis
• Sach-SW: FitzHugh-Nagumo model
• Sach-SW: global behaviour of solution branches
• Sach-SW: instability
• Sach-SW: pattern formation
• Sach-SW: reaction-diffusion-ODE system
• Sach-SW: steady states
• K10plus-PPN: 167209741X

Abstract

In this paper, we consider a diffusion equation coupled to an ordinary differential equation with FitzHugh-Nagumo type nonlinearity. We construct continuous spatially heterogeneous steady states near, as well as far from, constant steady states and show that they are all unstable. In addition, we construct various types of steady states with jump discontinuities and prove that they are stable in a weak sense defined by Weinberger.The results are quite different from those for classical reaction-diffusion systems where all species diffuse.