Routes to extreme events in dynamical systems: Dynamical and Statistical Characteristics

Abstract

Intermittent large amplitude events are seen in the temporal evolution of a state variable of many dynamical systems. Such intermittent large events suddenly start appearing in dynamical systems at a critical value of a system parameter and continues for a range of parameter values. Three important processes of instabilities, namely, interior crisis, Pomeau-Manneville intermittency and the breakdown of quasiperiodic motion, are most common as observed in many systems that lead to such occasional and rare transitions to large amplitude spiking events. We characterize these occasional large events as extreme events if they are larger than a statistically defined significant height. We present two exemplary systems, a single system and a coupled system to illustrate how the instabilities work to originate as extreme events and they manifest as non-trivial dynamical events. We illustrate the dynamical and statistical properties of such events.

References in corpus (7)

• Instabilities, breathers and rogue waves in optics
• Route to extreme events in excitable systems
• Intermittent large deviation of chaotic trajectory in Ikeda map: Signature of extreme events
• Two-dimensional dissipative rogue waves due to time-delayed feedback in cavity nonlinear optics
• Understanding the origin of extreme events in El Niño-Southern Oscillation
• Predictability of Extreme Intensity Pulses in Optically Injected Semiconductor Lasers
• Early warning signal for interior crises in excitable systems

Cited by in corpus (3)

• Extreme events in globally coupled chaotic maps
• Transition to hyperchaos: Sudden expansion of attractor and intermittent large-amplitude events in dynamical systems
• Instabilities in quasiperiodic motion lead to intermittent large-intensity events in Zeeman laser