Cu-Doped TiO₂₋ <i> _x </i> Nanoscale Memristive Applications in Chaotic Circuit and True Random Number Generator

TiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> has attracted significant attention as a prototypical material for memristors. In this article, a Cu-doped TiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">₋_x</i> nanoscale memristor with a structure of Ti/TiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2-</sub> <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">_x</i> :Cu/Cu is built, whose faithful mathematical model is established based on the memristive behaviors and its switching mechanism. Using this model, a chaotic system is constructed and its complex dynamics are investigated by numerical simulations. Furthermore, hardware experiments are also designed to verify the model in a chaotic circuit. The chaotic attractors obtained by simulations and hardware experiments are consistent, demonstrating the reliable performance of the Ti/TiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2-</sub> <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">_x</i> :Cu/Cu memristor and the correctness of its mathematical model. The processes of memristor from manufacture and mathematical modeling to its verification in a chaotic circuit are presented.