Applying the Conley index to fast-slow systems with one slow variable and an attractor

DOI10.1216/RMJ-2008-38-4-1177zbMath1162.34040MaRDI QIDQ1011055

William M. Kinney

Publication date: 7 April 2009

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

singular perturbationattractorConley indexHodgkin-Huxleyfast-slow system

Mathematics Subject Classification ID

Neural biology (92C20) Qualitative investigation and simulation of ordinary differential equation models (34C60) Attractors of solutions to ordinary differential equations (34D45) Index theory for dynamical systems, Morse-Conley indices (37B30) Singular perturbations for ordinary differential equations (34E15) Relaxation oscillations for ordinary differential equations (34C26)

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Symmetric bursting behaviors in the generalized FitzHugh-Nagumo model, Spike-adding canard explosion in a class of square-wave bursters

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