Hodgkin-Huxley equations implies Edge of Chaos Kernel

Abstract

This paper exposes Hodgkin-Huxley's "time-varying conductance"as an ill-conceived conceptual blunder and identifies a fundamental new physical concept dubbed "Edge of Chaos Kernel"as nature's optimal mechanism for creating an "action potential,"aka "all-or-none"response. As a bonus, it also offers a precise characterization of the heretofore unresolved notion of excitability, which in turn finally resolves Galvani's 240 year old enigma on the physical mechanism which gives rise to a near-abrupt all-or-none phenomenon, triggered by a global saddle-node bifurcation where a stable and an unstable periodic orbit grows in size while evolving their shape, ever so gently, so as to morph onto each other, until they became a single orbit, in high-dimensional state space. Even more intriguing is the Edge of Chaos Kernel's humble incarnation from the Chua's Riddle, and its innate ability to exhibit both Turing instability and the yet unresolved Smale's paradox.