Extreme and critical transition events in the memristor based Li\xe9nard system

S Leo Kingston,K Suresh,T Kapitaniak,K Thamilmaran

doi:10.1140/epjst/e2020-900165-1

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.

Highlights

Studies on extreme events (EEs) received notable attention in the last few decays owing to their catastrophic impact on nature and society [1]
A new class of extreme events has been identified in dissipative dynamical systems with discontinuous boundaries, where extreme events arise due to stick-slip dynamics [7]
We studied the extreme and critical transition events in the memristor based driven Lienard system

Summary

Introduction

Studies on extreme events (EEs) received notable attention in the last few decays owing to their catastrophic impact on nature and society [1]. The memristor based Lienard system exhibits multiple periodic or chaotic attractors for the fixed system parameters with the different choice of initial conditions. The well familiar nonlinear models such as van der Pol, Rossler, Chua’s circuit, Belousov-Zhabotinsky, and many other systems exhibit periodic or chaotic attractors for the typical choice of system parameters These attractors located as the neighborhood of its unstable fixed point are denoted as self excited attractors. When introducing the memristor in standard nonlinear models such as Lorenz and Rossler oscillators, the fixed point of the system disappeared, which leads to the emergence of hidden attractors This is an important observation since the above mentioned systems widely used for several engineering applications [27].

Model system

Extreme events

Critical transition event

Multistability

Hidden attractors in driven Lienard system

Conclusion