Oscillatory Growth: A Phenomenological View

TL;DR

This paper introduces phenomenological models to describe systems exhibiting oscillatory growth, distinguishing between constant and varying amplitude oscillations, and analyzing the effects of damping and parameter variations.

Contribution

It proposes two new phenomenological classes for oscillatory growth, including damping effects, and explores how parameters influence oscillation behavior.

Findings

Identified terms responsible for damping in oscillatory systems.

Analyzed how oscillation amplitude varies with system parameters.

Provided a framework for experimental data analysis of oscillatory growth.

Abstract

In this communication, the approach of phenomenological universalities of growth are considered to describe the behaviour of a system showing oscillatory growth. Two phenomenological classes are proposed to consider the behaviour of a system in which oscillation of a property may be observed. One of them is showing oscillatory nature with constant amplitude and the other represents oscillatory nature with a change in amplitude. The term responsible for damping in the proposed class is also been identified. The variations in the nature of oscillation with dependent parameters are studied in detail. In this connection, the variation of a specific growth rate is also been considered. The significance of presence and absence of each term involved in phenomenological description are also taken into consideration in the present communication. These proposed classes might be useful for the experimentalists to extract characteristic features from the dataset and to develop a suitable model consistent with their data set.