Phenomenological approach to describe oscillatory growth or decay in different dynamical systems

Abstract

The approach of the phenomenological universalities of growth is considered to describe the behaviour of a system showing an oscillatory growth. Two phenomenological classes are proposed to consider the oscillatory behaviour of a system. 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 decay (or growth) in amplitude in the proposed class is also been identified. The variations in the nature of oscillation with the dependent parameters are studied in this communication. In this connection, the variation of a specific growth rate is also been considered. The significance of the presence and the absence of each term involved in the phenomenological description are also taken into consideration. These proposed classes might be useful for the experimentalists to extract a characteristic feature from the data set and to develop a suitable model consistent with their data set.

Role of specific growth rate in the development of different growth processes

“…It has been shown in the dimensionless analysis that a truncated series up to third terms can produce oscillatory growth (or decay). When the second terms of the same truncated series is zero, it can produce sustained oscillation [49].…”