Extreme and critical transition events in the memristor based Liénard system

Abstract

We study extreme and critical events in the forced Liénard systems with charge control memristor. It has been found that the system exhibits hidden attractors either in the absence or presence of an external sinusoidal force. We give evidence that these attractors play a crucial role in the appearance of critical events. We attempt to explain the mechanism leading to the emergence of catastrophic transitions. Finally, we present that the observed critical transitions are typical for memristor based models and understanding of them gives some insight on how to avoid these types of devastating events at the time of the device fabrication process.

Transition to hyperchaos and rare large-intensity pulses in Zeeman laser

“…Extreme events have more complex characteristics features in their dynamical as well as statistical properties than the typical chaotic motion. Localized dynamical instabilities [35,36], namely, interior-crisis-induced intermittency [37][38][39][40], Pomeau-Manneville (PM) intermittency [37,41,42], breakdown of quasiperiodic motion [35,43], and quasiperiodic intermittency [43], are involved in the triggering of extreme events in a wide variety of nonlinear systems. Noise-induced attractor hopping in a multistable system [34], and instability of in-phase [44] and antiphase synchronization [42,45] in coupled systems can also originate extreme events.…”

Chaos in fractional system with extreme events

“…Authors observed extremely large amplitude oscillations in one of the system state variables when changing amplitude and the frequency of the forced signal. Extreme and critical transition events were found in Liénard system with memristor [ 21 ]. Extreme events and spatiotemporal chaos were measured in a microcavity laser [ 22 ].…”

Suppression of extreme events and chaos in a velocity-dependent potential system with time-delay feedback

“…Their occurrences have been reported in several dynamical systems. To name a few, we cite FitzHugh-Nagumo oscillators, Linéard system, Hindmarsh-Rose model, micromechanical system, memristor-based Liénard system, climatic models, electronic circuits, coupled Ikeda map, network of moving agents, network of Josephson junctions, dispersive wave models, Ginzburg-Landau model and nonlinear Schrödinger equation [4,5,8,[12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]. These events also appear in the form of optical rogue waves in lasers and optical fibers [6,7,28,29] and they have also been reported in experiments such as epileptic EEG studies in rodents, annular wave flume, and climatic studies [8,30,31].…”