The Simplest Memristor Oscillator is blessed with an Edge of Chaos Kernel

This paper presents a novel concept that the simplest memristor oscillator designed with the series connection of positive temperature coefficient (PTC) and negative temperature coefficient (NTC) memristors possesses an inherent property referred to as the “edge of chaos kernel”, hidden inside the small-signal equivalent circuit serves as an optimal mechanism for inducing a periodic oscillation. Furthermore, it is also demonstrated that the edge of chaos kernel, originated from Chua’s riddle and characterized by negative resistance (R < 0) and negative inductance (L < 0), exhibits potential stability but becomes unstable upon the addition of dissipative resistance or inductor component. This paper outlines the discoveries concerning the properties and behavior of the edge of chaos kernel circuit in the elementary memristor oscillator as well as the potential application in voltage control sensing circuit, elucidating its significance in nonlinear dynamics.