Phenomenological approach for describing environment dependent growths

Different classes of phenomenological universalities of environment dependent growths have been proposed. The logistic as well as environment dependent West-type allometry based biological growth can be explained in this proposed framework of phenomenological description. It is shown that logistic and environment 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. It is also established that environment independent and enviornment dependent biological growth processes lead to the same West-type biological growth equation. 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. In addition, some other phenomenological descriptions have been examined in this proposed framework and graphical representations of variation of different parameters involved in the description are executed.