Dynamical systems theory has emerged as an interdisciplinary area of research to
characterize the complex dynamical transitions in real-world systems. Various nonlinear …

Identifying the governing parameters of self-sustained oscillation is crucial for the diagnosis,
prediction and control of thermoacoustic instabilities. In this paper, we propose and validate …

We derive and numerically validate a low-order oscillator model to capture the stochastic
dynamics of a prototypical thermoacoustic system (a Rijke tube) undergoing a subcritical …

In this work, we numerically investigate the dynamics of a prototypical thermoacoustic
system, the generalized Van der Pol oscillator, in the presence of additive noise of varying …

A Hopf bifurcation, where a fixed-point solution loses stability and a limit cycle is born, is
prevalent in many nonlinear dynamical systems. When a system prior to a Hopf bifurcation is …

Intense thermoacoustic oscillations may lead to severe deterioration due to the induced
intolerable damage to combustors. A better understanding of unstable behaviors is …

Combustion systems are exposed to intrinsic and extrinsic noise arising from various
sources. Contrasting the conventional viewpoint of treating noise as signal contamination …

In this chapter, we study the bifurcation characteristics of a laminar thermoacoustic system
through the application of dynamical system theory. We restrict our discussions to two simple …

Thermoacoustic combustion instabilities arising from the interaction between the unsteady
heat release rate and the combustor acoustic mode continue to hamper the development …