Edge of Chaos Kernel and neuromorphic dynamics of a locally-active memristor

Abstract

Edge of Chaos Kernel (EOCK), the crown jewel of edge of chaos, is a nature’s optimal mechanism for creating action potentials, which can be exploited to uncover the neuromorphic dynamics of memristors. A memristor blessed with an EOCK, which can emulate the neuromorphic behaviors of biological neurons, is a natural candidate to be applied in neuromorphic computing. This paper proves that a first-order memristor blessed with an EOCK has a pole in the open left half plane (LHP), and presents a simple method for testing if a generic voltage-controlled first-order memristor has an EOCK using only its first-order Taylor series expansion coefficients. This paper presents, for the first time, that locally active voltage-controlled generic memristors contain an EOCK. Also, this paper designs a theoretical memristor model blessed with an EOCK, and constructs a memristive circuit for observing the relationship between the EOCK and neuromorphic behaviors. The memristor blessed with an EOCK generates some well-known neuromorphic behaviors, further verify the innate ability of Edge of Chaos Kernel to exhibit the complex phenomena. This paper pave the way towards further expounding the generating mechanism of the action potential from the perspective of circuit.