Local active memristive oscillator enables controllable complex behaviours and frequency domain extraction.

Physical non-linearities near the Mott transition exhibit substantial potential for neuromorphic computing. The complex computational behaviour stems from their intrinsic local active characteristics. Most studies focus on decay dynamics or regular oscillations, treating Mott devices primarily as simple threshold elements. Challenges remain in connecting measurable material properties to more complex device dynamics and their control methods through a unified theoretical model. Here, we develop a thermodynamic compact model for vanadium oxide devices based on electrical measurements and the local active principle. Utilizing the non-linearities near the Mott transition, we propose an injection-based control method to regulate behaviours of non-linear oscillators, such as frequency division, stochastic oscillations and frequency locking. Finally, a single device operating at the edge of chaos demonstrates exceptional capability in extracting information in the frequency domain within a physical computing framework, achieving performance equivalent to a two-layer convolutional neural network on the same task. This work facilitates a paradigm shift from traditional local passive devices to local active devices, bridging the physical non-linearities, circuit dynamics and computational theory to advance dynamic neuromorphic computing.