Hodgkin–Huxley equations implies Edge of Chaos Kernel
Leon O. Chua
Abstract
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.