Organic Electrochemical Neurons: Nonlinear Tools for Complex Dynamics.

Hybrid oscillator architectures that combine feedback oscillators with self-sustained negative resistance oscillators have emerged as promising platforms for artificial neuron design. In this work, we introduce a modeling and analysis framework for amplifier-assisted organic electrochemical neurons leveraging nonlinear dynamical systems theory. By formulating the system as coupled differential equations describing membrane voltage and internal state variables, we identify the conditions for self-sustained oscillations and characterize the resulting dynamics through nullclines, phase space, and bifurcation analysis, providing complementary insight into standard circuit-theoretic arguments of the operation of oscillators. Our simplified yet rigorous model enables tractable analysis of circuits integrating classical feedback components (e.g., operational amplifiers) with devices exhibiting negative differential resistance such as organic electrochemical transistors (OECTs). This approach reveals the core mechanisms behind oscillation generation, demonstrating the utility of dynamic systems theory in understanding and designing complex hybrid circuits. Beyond neuromorphic and bioelectronic applications, the proposed framework offers a generalizable foundation for developing tunable biologically inspired oscillatory systems for sensing, signal processing, and adaptive control.