The Duffing adaptive oscillator

As a subset of nonlinear oscillators, adaptive oscillators are often constructed by appending additional dynamic states to a nonlinear oscillator. Adaptive oscillators have dynamic states that can learn and store information. This type of dynamic learning has received relatively little attention, but it is an attractive method for many types of systems that require data processing in real-world applications. As an example, adaptive oscillators have been shown to function as physical reservoir computers, in which adaptation can be used for both self-learning and multiplex-free morphable logic gates. In this paper, an adaptive oscillator is constructed from the Duffing oscillator for the first time. The dynamics of the hardening monostable, softening monostable, and bistable Duffing oscillator is considered. As the Duffing oscillator is a common model for a wide range of physical systems, it is likely that adaptation could be extended to many of these systems for enhanced functionality.