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Conditions for periodic solutions of volterra differential systems

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Abstract

As a contribution to the discussion of oscillatory models for interacting species it is shown that two-species Volterra models can never have limit cycles, and a complete enumeration is given of conditions which the parameters of these models must satisfy in order that a part of the phase space be filled with a family of closed curves; sketches of phase portraits are also given. These results complement and correct older results by Bautin and by Coppel on quadratic differential systems. The paper opens with a brief discussion of some more practical aspects of the ecological application of oscillatory models.

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Authors and Affiliations

  1. Biomathematics Program, Department of Statistics, North Carolina State University, 27607, Raleigh, NC, USA

    H. Robert van der Vaart

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  1. H. Robert van der Vaart
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van der Vaart, H.R. Conditions for periodic solutions of volterra differential systems. Bltn Mathcal Biology 40, 133–160 (1978). https://doi.org/10.1007/BF02461432

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  • DOI: https://doi.org/10.1007/BF02461432

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