Extreme and Dragon-King Events in a Discrete Neuron Model

This study investigates the behavior of the Izhikevich discrete neuron model across various parameter configurations. Bifurcation diagrams and Lyapunov exponents are utilized to examine the impact of these parameters on the behavior of the system. The study specifically identifies important parameter ranges in which the attractor undergoes a sudden expansion, displaying characteristics of extreme events. Within the system, two distinct categories of extreme events can be identified: rare occurrences of small probability events located in the tail of the probability distribution and Dragon-King (DK) events, which possess a high probability amplitude. DK events are verified through the use of the DK test. The research concludes by examining the practical ramifications of these findings. The significance of forecasting and controlling extreme events in intricate systems is underscored, along with the cruciality of identifying their happening.