PDR-Enabled Edge of Chaos in Locally Active Memristors and Their Oscillators

Locally active memristors (LAMs) biased in the edge of chaos (EOC) regime are conventionally characterized by negative differential resistance (NDR). However, based on the theory of local activity and EOC, we propose that NDR behavior constitutes a sufficient rather than a necessary condition for the emergence of the EOC regime. In this paper, we systematically investigate EOC behaviors in different classes of memristors. Mathematical models of a first-order extended memristor and a second-order generic memristor are developed, revealing that the EOC regime can also arise in regions exhibiting positive differential resistance (PDR). Based on the first-order model, a single-topology memristive oscillator is designed. In contrast, by exploiting the dual local reactance properties of the second-order model, namely that it possesses both local capacitive and local inductive properties at a same operating point, dual-topology memristive oscillators (memristor-inductor and memristor-capacitor types) are developed. Using EOC Principle and small-signal analysis, the relationship between NDR/PDR domain and EOC regime for various memristor types is rigorously clarified. Furthermore, we analyze how PDR- and NDR-based EOC regimes influence oscillator topology design, parameter constraints (capacitance or inductance), and operational frequency ranges. Finally, a representative second-order LAM emulator based on the PDR-type EOC is implemented, and hardware experiments validate the theoretical and simulation results. This work provides a theoretical basis for searching for novel nanoscale locally active devices with PDR-based EOC regime.