ABSTRACT

This chapter exposes Hodgkin–Huxley’s “time-varying conductance” as an ill-conceived conceptual blunder and identifies a fundamentally 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 definition of the heretofore unresolved notion of excitability, which in turn finally resolves Galvani’s 242-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 4-dimensional state space. Even more intriguing is the Edge of Chaos Kernel’s humble incarnation from Chua’s Riddle, and its innate ability to exhibit both Turing instability and Smale’s paradox.