Date of Award

31-8-2024

Document Type

Thesis

School

School of Electrical & Electroncis Engineering

First Advisor

Dr.R.Suresh

Keywords

Extreme Events, Nonlinear Oscillators, Parametric Excitation

Abstract

This comprehensive PhD thesis immerses itself in the intricate world of dynamical systems, aiming to understand, characterize, and develop innovative mitigation strategies for rare and extreme events occurring within diverse nonlinear oscillatory models. The term "events" spans a broad array of occurrences within defined systems, with "rare events" standing out as infrequent outliers or deviations from the norm.

Rare events span various disciplines such as oceanography, climate studies, biology, economics, ecology, encompassing phenomena like rogue waves, floods, cyclones, earthquakes, and financial crises. Recognized for their potential to cause substantial harm to both society and the environment, these events are widely acknowledged as extreme events.

The journey into the dynamical study of extreme events originated with early research on rogue waves, utilizing the nonlinear Schrodinger equation as a foundational model. This research highlighted the significance of modulation instability in the production of rogue waves, emphasizing their rare occurrence and the resulting long-tailed statistical distribution of extreme events. Subsequent investigations extended to various domains, employing partial differential equations to model extreme occurrences in optics, hydrodynamics, chemical sciences, and finance.

Recent research delves into rare, recurrent, and large amplitude oscillations marked as extreme events within nonlinear dynamical systems, employing ordinary differential equations to simulate extreme events in physical, biological, and sociological systems. The primary objective is to unravel novel mechanisms and routes in nonlinear oscillators subjected to parametric excitation and external forcing. The overarching goal is to not only enhance our understanding but also pave the way for effective mitigation strategies.

The initial section of the thesis meticulously explores bursting dynamics in the Rayleigh-Lienard hybrid system, revealing periodic and chaotic bursting oscillations classified as extreme events. The concept of a pulse-shaped explosion is introduced, validated through the transformation of the system into a fast-slow system and utilizing a single slow variable. The study extends to a Mathews-Lakshmanan oscillator model, identifying distinct bifurcation routes leading to sudden, intermittent chaotic spikes. Comprehensive investigations are conducted not only to identify the development and mechanism of these occurrences but also to anticipate and proactively manage extreme events.

The second part of the thesis shifts its focus towards finding practical methods to mitigate extreme events. It delves into the dynamics of a periodically forced anharmonic oscillator and a forced Lienard oscillator with asymmetric potential wells. Linear damping emerges as a crucial mechanism for suppressing extreme events, providing valuable insights for control within the systems. The outcomes of these studies contribute significantly to advancing our comprehension of extreme events in diverse nonlinear oscillators, offering a robust foundation for guiding future research in this fascinating and complex field.

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