J. M. Cushing

Research output: Contribution to journalArticlepeer-review

196 Scopus citations


The general system of differential equations describing predator-prey dynamics is modified by the assumption that the coefficients are periodic functions of time. By use of standard techniques of bifuraction theory, as well as a recent global result of P. H. Rabinowitz, it is shown that this system has a periodic solution (in place of an equilibrium) provided the long term time average of the predator's net, uninhibited death rate is in a suitable range. The bifurcation is from the periodic solution of the time-dependent logistic equation for the prey (which results in the absence of any predator). Numerical results which clearly show this bifurcation phenomenon are briefly discussed.

Original languageEnglish (US)
Pages (from-to)82-95
Number of pages14
JournalSIAM Journal on Applied Mathematics
Issue number1
StatePublished - 1977

ASJC Scopus subject areas

  • Applied Mathematics


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