Publication date: 15th December 2025
Oscillatory dynamics are a cornerstone of computational physics and emerging neuromorphic hardware, where information processing relies on synchronization and collective temporal behavior. Despite their importance, predicting the onset of self-sustained oscillations in physical devices remains a nontrivial task, particularly in systems governed by strong nonlinearities and local activity. In this work, we establish practical and physically grounded criteria for the emergence of oscillations in neuronic units by applying bifurcation theory to systems exhibiting nonlinear and locally active behavior, including both S-type and N-type negative differential resistance [1].
By analyzing stationary states through the Jacobian matrix and tracking stability transitions in the trace–determinant plane, we systematically identify the parameter regimes that give rise to Hopf bifurcations and sustained oscillatory dynamics. These analytical predictions are corroborated by numerical simulations, revealing clear connections between device parameters, oscillation frequency, and stability. In addition, we identify characteristic signatures in the impedance spectra associated with the onset of oscillations, providing experimentally accessible markers of dynamical transitions.
This unified dynamical framework enables reliable prediction and control of oscillatory behavior across a broad class of ionic–electronic and memristive devices, and offers concrete design guidelines for the development of robust, tunable neuromorphic oscillators and scalable oscillator-based computing networks.
We thank the MENEU project (20250002) funded by the Universitat Politècnica de València
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