DYNAMICS OF POPULATIONS SUBJECT TO SELECTIVE HARVEST: UNIQUENESS, STABILITY, AND PERIODIC BEHAVIOUR.

Anthony S.T. Chiang, Robert W. Thompson

Research output: Contribution to journalArticlepeer-review

Abstract

We develop here the criteria for the existence and uniqueness of steady state points, stability of the steady states, and the possibility of periodic behavior of a population, which is governed by a known age-dependent specific reproduction function, and an externally controlled age-dependent removal function. In general, it appears that uniqueness of the steady state is not guaranteed, the steady state points are metastable, and periodicity can arise only if the removal function is periodic or if the removal and maternity functions are periodic. Lastly, we prove the conclusion, previously conjectured by M. E. Gurtin and R. C. MacCamy, that no periodic solution exists for systems having an age-dependent maternity function and a density-dependent removal function.

Original languageEnglish
Pages (from-to)295-302
Number of pages8
JournalJournal of the Chinese Institute of Chemical Engineers
Volume17
Issue number5
StatePublished - Sep 1986

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