Rare Large-Amplitude Events in an Elementary Diode-Based Jerk Circuit: Theory and Experiment

This paper reports the emergence of rare, large-amplitude events in an extremely simple autonomous jerk circuit employing a single semi-conductor diode as its only nonlinear element. The governing equation corresponds to a third-order jerk system with exponential nonlinearity. Thanks to numerical simulations and theoretical analysis, we characterize the system’s dynamics using two-parameter Lyapunov exponent plots, bifurcation diagrams, and phase portraits. Our study reveals that these rare large-amplitude events emerge particularly at an interior crisis point. Statistical analysis confirms their rarity, with events detected at thresholds ranging from 4 to 10 standard deviations above the mean. Experimental measurements from a hardware realization of the circuit corroborate the salient features predicted by the theoretical study. To the best of our knowledge, this model represents the simplest chaotic jerk circuit reported to date capable of exhibiting such pronounced, rare large-amplitude events. Its elementary design, hinging on a single diode, makes it a paradigm of interest for fundamental studies of crisis-induced dynamics and a versatile building block for investigating complex phenomena in more advanced applications, such as coupled oscillator networks.