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This paper introduces an innovative graphical analysis tool for investigating the dynamics of Memristor Cellular Nonlinear Networks (M-CNNs) featuring 2nd-order processing elements, known as M-CNN cells. In the era of specialized hardware catering to the demands of intelligent autonomous systems, the integration of memristors within Cellular Nonlinear Networks (CNNs) has emerged as a promising paradigm due to their exceptional characteristics. However, the standard Dynamic Route Map (DRM) analysis, applicable to 1st-order systems, fails to address the intricacies of 2nd-order M-CNN cell dynamics, as well the 2nd-order DRM (DRM2) exhibits limitations on the graphical illustration of local dynamical properties of the M-CNN cells, e.g. state derivative's magnitude. To address this limitation, we propose a novel integration of M-CNN cell vector field into the cell's phase portrait, enhancing the analysis efficacy and enabling efficient M-CNN cell design. A comprehensive exploration of M-CNN cell dynamics is presented, showcasing the utility of the proposed graphical tool for various scenarios, including bistable and monostable behavior, and demonstrating its superior ability to reveal subtle variations in cell behavior. Through this work, we offer a refined perspective on the analysis and design of M-CNNs, paving the way for advanced applications in edge computing and specialized hardware., Comment: Presented at the 18th IEEE International Workshop on Cellular Nanoscale Networks and their Applications (CNNA'23) and the 8th Memristor and Memristive Symposium

In this theoretical study, we focus on the high-frequency response of the electrothermal NbO2-Mott threshold switch, a real-world electronic device, which has been proved to be relevant in several applications and is classified as a volatile memristor. Memristors of this kind, have been shown to exhibit distinctive non-linear behaviors crucial for cutting-edge neuromorphic circuits. In accordance with well-established models for these devices, their resistances depend on their body temperatures, which evolve over time following Newton's Law of Cooling. Here, we demonstrate that HP's NbO2-Mott memristor can manifest up to three distinct steady-state oscillatory behaviors under a suitable high-frequency periodic voltage input, showcasing increased versatility despite its volatile nature. Additionally, when subjected to a high-frequency periodic voltage signal, the device body temperature oscillates with a negligible peak-to-peak amplitude. Since, the temperature remains almost constant over an input cycle, the devices under study behave as linear resistors during each input cycle. Based on these insights, this paper presents analytical equations characterizing the response of the NbO2-Mott memristor to high-frequency voltage inputs, demarcating regions in the state space where distinct initial conditions lead to various asymptotic oscillatory behaviors. Importantly, the mathematical methods introduced in this manuscript are applicable to any volatile electrothermal resistive switch. Additionally, this paper presents analytical equations that accurately reproduce the temperature time-waveform of the studied device during both its transient and steady-state phases when subjected to a zero-mean sinusoidal voltage input oscillating in the high-frequency limit.