Self-sustained oscillatory devices are emerging as key building blocks for iontronic, neuromorphic, and unconventional computing architectures, where information can be processed directly through the nonlinear dynamics of materials and devices. In these systems, variables such as phase, frequency, synchronization, entrainment, and spiking activity can encode and transform information in real time, enabling new approaches to tasks such as optimization, pattern classification, and temporal inference. [1] A common route to generate self-oscillations in electronic and iontronic devices is the presence of negative differential resistance (NDR), which provides the active feedback required to destabilize a stationary state and sustain a limit-cycle oscillation. However, the observation of NDR alone is not sufficient to predict oscillatory behavior, since the onset of instability depends on the coupling between the active material dynamics, internal relaxation processes, and external circuit elements. [2,3]

Here, we show that impedance spectroscopy provides a powerful experimental framework to identify, interpret, and predict the emergence of self-sustained oscillations in S-type NDR devices. Using a thyristor-based oscillator as a model system, we first demonstrate that frequency-domain measurements reveal direct signatures of nonlinear dynamical phenomena such as stability loss, Hopf bifurcation, autonomous oscillations, entrainment, phase locking, and divergence of the impedance response near the oscillatory threshold. By mapping impedance spectra onto an equivalent-circuit representation, we connect experimentally accessible circuit parameters with the local linearized dynamics of the system. This establishes a bridge between impedance spectroscopy, nonlinear bifurcation theory, and classical control concepts such as transfer-function stability criteria. [4]

Building on this framework, we further show that impedance spectroscopy can be used not only to detect dynamical instabilities, but also to reconstruct the experimental stability map of a self-oscillatory device. From the equivalent-circuit parameters, we define a stability time constant τ_s obtained from the parallel coupling of the dynamic relaxation branches of the system. This time constant is directly related to the trace of the Jacobian of the underlying dynamical equations, providing an experimental criterion for whether small perturbations around a stationary state are damped or amplified. Its sign therefore determines the transition between stable operation and self-sustained oscillations, while its zero-crossing identifies the bifurcation boundary.

By varying the external capacitance coupled to the device, we experimentally construct the current–capacitance (I₀, C₀) bifurcation diagram and validate the predicted stable and oscillatory regimes with time-domain voltage measurements. This approach allows the stability landscape of the device to be mapped without requiring a complete microscopic nonlinear model. More broadly, it enables the identification of the physical or physico-chemical branch responsible for the destabilizing feedback, including ionic motion, delayed conductance activation, interfacial charge storage, or other emergent material processes.

These results establish impedance spectroscopy as a stability-resolved diagnostic tool for iontronic and mixed ionic-electronic devices. The method provides a practical route to discover hidden instabilities, design oscillatory regimes, and control nonlinear dynamics in emerging material-based hardware for neuromorphic and physical computing. [3]