INVERTEDLY-BIFURCATING SELF-OSCILLATIONS IN THE MODIFIED HODGKIN-HUXLEY EQUATIONS.

Bifurcation characteristics in the modified Hodgkin-Huxley equations are investigated in detail on the basis of a recently presented theory, which can describe normally bifurcating as well as invertedly-bifurcating hard-mode instabilities. An algebraic-processing computer language was used to get analytic expressions in perturbative calculations up to the fifth order. The present theoretical results can describe the full bifurcation diagram for the case where normally and invertedly bifurcation diagram for the case where normally and invertedly bifurcating instability points coexist closely. It is also shown that the present theory can describe even an interesting example of the bifurcation diagram which is formed by a single continuous closed branch composed of unstable and stable self-oscillations without any instability point.