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Qualitative properties of a niche-model

Author

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  • Mainik, J.
  • Ortlieb, C.P.

Abstract

Within the framework of ecological systems analysis, the potential of niche formation plays an essential role, particularly in relation to the conditions of permanence or extinction of individual species. In this realm the model developed by Greve [Helgoländer Meeresuntersuchungen 49, (1995) 811–820] in his study of possibilities of predicting marine populations represents an interesting approach. This model, which consists of a system of coupled differential equations applies an age differentiation with complex relations between the populations. The purpose of this paper is to perform a qualitative analysis of this model. The main questions are the conditions of extinction, boundedness and permanence as well as the conditions of the existence and uniqueness of stationary solutions. Our analysis provides both a notion of the model's behaviour and a mathematical evaluation of this model. The preliminary results are positive and encouraging.

Suggested Citation

  • Mainik, J. & Ortlieb, C.P., 1999. "Qualitative properties of a niche-model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 49(6), pages 353-374.
    • Handle: RePEc:eee:matcom:v:49:y:1999:i:6:p:353-374
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