Shyamolina Ghosh

Chemical oscillator as a generalized Rayleigh oscillator

We derive the conditions under which a set of arbitrary two dimensional autonomous kinetic equations can be reduced to the form of a generalized Rayleigh oscillator which admits of limit cycle solution. This is based on a linear transformation of field variables which can be found by inspection of the kinetic equations. We illustrate the scheme with the help of several chemical and bio-chemical oscillator models to show how they can be cast as a generalized Rayleigh oscillator.

Noisy-flow-induced instability in a reaction-diffusion system

We consider a generic reaction-diffusion-advection system where the flow velocity of the advection term is subjected to dichotomous noise with zero mean and Ornstein-Zernike correlation. A general condition for noisy-flow-induced instability is derived in the flow velocity-correlation rate parameter plane. Full numerical simulations on Gierer-Meinhardt model with activator-inhibitor kinetics have been performed to show how noisy differential flow can lead to symmetry breaking of a homogeneous stable state in the presence of noise resulting in traveling waves.

Parametric spatiotemporal oscillation in reaction-diffusion systems.

We consider a reaction-diffusion system in a homogeneous stable steady state. On perturbation by a time-dependent sinusoidal forcing of a suitable scaling parameter the system exhibits parametric spatiotemporal instability beyond a critical threshold frequency. We have formulated a general scheme to calculate the threshold condition for oscillation and the range of unstable spatial modes lying within a V-shaped region reminiscent of Arnolds tongue. Full numerical simulations show that depending on the specificity of nonlinearity of the models, the instability may result in time-periodic stationary patterns in the form of standing clusters or spatially localized breathing patterns with characteristic wavelengths. Our theoretical analysis of the parametric oscillation in reaction-diffusion system is corroborated by full numerical simulation of two well-known chemical dynamical models: chlorite-iodine-malonic acid and Briggs-Rauscher reactions.

Rayleigh-type parametric chemical oscillation

We consider a nonlinear chemical dynamical system of two phase space variables in a stable steady state. When the system is driven by a time-dependent sinusoidal forcing of a suitable scaling parameter at a frequency twice the output frequency and the strength of perturbation exceeds a threshold, the system undergoes sustained Rayleigh-type periodic oscillation, wellknown for parametric oscillation in pipe organs and distinct from the usual forced quasiperiodic oscillation of a damped nonlinear system where the system is oscillatory even in absence of any external forcing. Our theoretical analysis of the parametric chemical oscillation is corroborated by full numerical simulation of two well known models of chemical dynamics, chlorite-iodine-malonic acid and iodine-clock reactions.