Journal
NONLINEAR DYNAMICS
Volume 97, Issue 1, Pages 571-582Publisher
SPRINGER
DOI: 10.1007/s11071-019-04998-4
Keywords
Solitary solution; Hodgkin-Huxley model; Generalized differential operator; Heteroclinic bifurcation; 35B32; 35C08
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This paper presents necessary and sufficient conditions for the existence of bright/dark solitary solutions in the Hodgkin-Huxley model. The second-order analytic solitary solutions are derived using the generalized differential operator technique. It is shown that the heteroclinic bifurcation in the Hodgkin-Huxley model yields a symmetry breaking effect. Trajectories of solitary solutions before the bifurcation lie on manifolds of one of the saddle points and the separatrix between periodic and non-periodic solutions. A new separatrix emerges after the heteroclinic bifurcationbut solitary solutions do not lie on this trajectory. This symmetry breaking effect is demonstrated using analytic and computational experiments.
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