Shortcuts to <i>Edge-of-Chaos</i> Domains of <i>Memristive</i> Circuits and <i>Historic Measurement</i> of Contiguous Triple-Branch <i>V – I Curve</i> of Chua Corsage Memristor

Locally-active memristors blessed with an edge-of-chaos domain, which can be destabilized for generating action potentials, are natural candidates for emulating biological neurons. Pinpointing the edge-of-chaos domain, where neuromorphic behaviors may occur, is important for studying neuromorphic dynamics of memristors. This paper proposes a short-cut method for locating the edge-of-chaos domains in two kinds of generic memristors, and in several typical memristive 1-port circuits using only the Jacobian matrix in terms of their equations. Taking the Chua Corsage Memristor (CCM) and several CCM-based memristive 1-port circuits as examples, we verify the proposed new methods, and calculates their edge-of-chaos domains. Also, we carry out a complete classification of all the parameter regions of the CCM and several CCM-based memristive 1-port circuits, namely the locally-passive, locally-active but unstable, and edge-of-chaos domains, under both voltage and frequency control. Near the calculated edge-of-chaos domain, we uncover some new neuromorphic behaviors. To confirm the physical interpretations and predictions of the edge-of-chaos theorem, this paper presents an inexpensive electronic circuit realization of the complete set of equations defining the CCM using only off-the-shelf circuit components. When this poor-man’s memristor is connected to various linear passive R, L, C circuits, and a battery, the resulting circuit can be tuned to generate action potentials, and a garden variety of neuromorphic phenomena, including chaos. But the highlight of this paper is reserved for the CCM itself where the world’s first oscilloscope picture of a contiguous self-intersecting triple-branch DC V–I curve of the CCM is displayed in real time.