Emergence of nonchaotic bursting extreme events in a quadratic jerk oscillator

Extreme events are intriguing phenomena that can manifest in various realistic scenarios. Understanding the circumstances under which they occur is crucial due to their potentially devastating impact. In contrast to prior studies that employed the jerk system to demonstrate chaotic behavior, hidden dynamics, and multistability, our investigation focuses on a complex quadratic jerk system to illustrate the emergence of extreme events. Our primary focus lies in discerning various bursting patterns such as periodic, quasi-periodic, strange nonchaotic, and chaotic with respect to the control parameter. Significantly, the transitions between these bursting dynamics are analyzed through bifurcation analysis and their corresponding Lyapunov exponents. Notably, the bifurcation analysis confirms the presence of extreme events by revealing a notable amplification in the signals maximum amplitude, which exceeds the extreme events critical threshold. Furthermore, we employ a two-parameter analysis to delineate regions corresponding to different bursting states, along with regions indicative of extreme events and non-extreme events phenomena. Interestingly, our observations pinpoint occurrences of extreme events within the nonchaotic domain. Consequently, we employ various statistical measures to confirm the presence of strange nonchaotic dynamics. Our results highlight the presence of extreme events in nonchaotic bursting in chaotic complex systems and provide insight into the complex interactions among dynamics in these systems.