Stability and oscillations in single-species processes with past memory†

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Abstract
Conditions for oscillations, non-oscillations and stability of single-species hereditary processes in biological, medical, physical and social sciences were derived by using elementary mathematical analysis. The obtained conditions are expressed in terms of rate functions and time-delays. They are algebraically simple and easy to compute. Certain classes of time-delays are both stabilizing and oscillizing agents, and some other classes of delays are only stabilizing agents. The usefulness of the oscillatory and stability analysis of single-species processes was demonstrated by exhibiting several well known examples of single-species processes in biological, medical, physical and social sciences in a coherent way.