Extreme events as early warning signals of crisis-induced escape in discrete neuronal system

We investigate the divergence of a bounded chaotic attractor and its early warning indicators in a discrete neuron model. As a control parameter is varied, the system undergoes a sequence of dynamical transitions, from quasiperiodic states to strange nonchaotic attractors (SNAs), then to chaos, and ultimately to escape, marked by the loss of bounded dynamics. These transitions are analyzed using bifurcation diagram and Lyapunov exponent. Importantly, the extreme events emerge through interior crises within certain chaotic regimes, where sudden expansions of the attractor occur, and their presence is confirmed through critical amplitude threshold and statistical analysis. As the parameter increases further, a boundary crisis causes the chaotic attractor to collide with its basin boundary, leading to divergence and unbounded behavior. The nature of the attractors is validated through Poincaré return map, power spectrum, correlation analysis, and the 0–1 test for chaos, while SNAs are identified via singular continuous spectrum and separation of nearby trajectories. In addition, a gated recurrent unit-based machine learning approach is employed to forecast extreme events, and its accuracy is evaluated using the root mean square error. Overall, the results reveal how interior and boundary crises serve as early warning signals for attractor divergence and escape in complex dynamical systems.