2010/10/30 by Panayiotis S. Georgiou, Sophia N. Yaliraki, Georgiou, Panayiotis S. +5 · 1 citation
Engineering · Mathematics · Neuroscience · Physics and Astronomy · #Advanced Memory and Neural Computing #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Neural dynamics and brain function #cond-mat.mes-hall #math.DS #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.1011.0060
11 pages, 12 figures
openalex publication_date 2010/10/30 · arxiv created 2011/07/17 · arxiv updated 2011/07/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a mathematical framework for the analysis of the input-output\ndynamics of externally driven memristors. We show that, under general\nassumptions, their dynamics comply with a Bernoulli differential equation and\nhence can be nonlinearly transformed into a formally solvable linear equation.\nThe Bernoulli formalism, which applies to both charge- and flux-controlled\nmemristors when either current- or voltage-driven, can, in some cases, lead to\nexpressions of the output of the device as an explicit function of the input.\nWe apply our framework to obtain analytical solutions of the i-v\ncharacteristics of the recently proposed model of the Hewlett-Packard memristor\nunder three different drives without the need for numerical simulations. Our\nexplicit solutions allow us to identify a dimensionless lumped parameter that\ncombines device-specific parameters with properties of the input drive. This\nparameter governs the memristive behavior of the device and, consequently, the\namount of hysteresis in the i-v. We proceed further by defining formally a\nquantitative measure for the hysteresis of the device for which we obtain\nexplicit formulas in terms of the aforementioned parameter and we discuss the\napplicability of the analysis for the design and analysis of memristor devices.\n