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Logistic growth; exogenous process; carrying capacity; metabolic cost.

In this communication, different classes of phenomenological universalities of carrying capacity dependent growth processes have been proposed. The logistic as well as carrying capacity-dependent West-type allometry-based biological growths can be explained in this proposed framework. It is shown that logistic and carrying capacity-dependent West-type growths are phenomenologically identical in nature. However, there is a difference between them in terms of coefficients involved in the phenomenological descriptions. Involuted Gompertz function, used to describe biological growth processes undergoing atrophy or a demographic and economic system undergoing involution or regression, can be addressed in this proposed environment-dependent description. It is also found phenomenologically that the energy intake of an organism depends on carrying capacity whereas metabolic cost does not depend on carrying capacity. In addition, some other phenomenologicaldescriptions have been examined in this proposed framework and graphical representations of variation of different parameters involved in the description are executed.

DIBYENDU BISWAS¹ SWARUP PORIA² SANKAR NARAYAN PATRA³

1. Department of Basic Science, Humanities and Social Science (Physics), Calcutta Institute of Engineering and Management, 24/1A, Chandi Ghosh Road, Kolkata 700 040, India
2. Department of Applied Mathematics, University of Calcutta, 92 APC Road, Kolkata 700 009, India
3. Department of Instrumentation Science, Jadavpur University, 188, Raja S.C. Mallick Road, Kolkata 700 032, India

Published

16 November 2016

Manuscript received

2 June 2015

Manuscript revised

11 February 2016

Accepted

24 February 2016

Early published

18 October 2016