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Behaviour of generalised logistic equations on time scales. (English) Zbl 1215.34055

Summary: We study the characteristics of generalised logistic and exponential functions on various time scales. The motivation behind this paper is that some populations are better modelled by exponential and logistic equations on a particular time scale. However, an unusual characteristic of some logistic equations on time scales is the possibility of producing negative output values, something that is impossible for a population. So, the focus of this paper is to analyse the generalised logistic equation and to give necessary conditions such that the output of these equations on time scales remains greater than zero for all points on the time scale.

MSC:

34C60 Qualitative investigation and simulation of ordinary differential equation models
34N05 Dynamic equations on time scales or measure chains
92D25 Population dynamics (general)
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