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Global stability of partially closed food-chains with resources

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Abstract

We consider the existence and global stability of aq-member equilibrium (1≤q≤n) in partially closed food-chains of lengthn having an abiotic component as resource. We observe that such existence demands bounds of resource supply rate and these bounds are weighted sums of interaction coefficients. Particular results of global sector-stability of partially feasible equilibria of simple food-chains obeying Lotka-Volterra dynamics are shown. Lastly the elasticity of such food-chains when a new species is introduced at the highest trophic level is investigated.

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Literature

  • Beretta, E. and V. Capasso. 1986. “On the General Structure of Epidemic System. Global Asymptotic Stability.”Comput. Math., Applic. A special journal issue in honor of Richard Bellman, in press.

  • Freedman, H. I. and P. Waltman. 1977. “Mathematical Analysis of Some Three-species Food-chain Models.”Mathl Biosci. 33, 257–276.

    Article  MATH  MathSciNet  Google Scholar 

  • Gard, T. C. 1980. “Persistence in Food Webs: Holling type Food Chain”Mathl Biosci. 49, 61–67.

    Article  MATH  MathSciNet  Google Scholar 

  • — 1982. “Top Predator Persistence in Differential Equations Model of Food Chain: the effects of Omnivory and external Forcing of Lower Trophic Levels.”J. Math. Biol. 14, 285–299.

    Article  MATH  MathSciNet  Google Scholar 

  • — and T. G. Hallam. 1979. “Persistence in Food Webs—I. Lotka-Volterra Food Chains.”Bull. math. Biol. 41, 877–891.

    Article  MATH  MathSciNet  Google Scholar 

  • Goh, B. S. 1978. “Sector Stability of a Complex Ecosystem Model.”Mathl Biosci. 40, 157–166.

    Article  MATH  MathSciNet  Google Scholar 

  • LaSalle, J. and S. Lefschetz. 1961.Stability of Liapunob Direct Method. New York: Academic Press.

    Google Scholar 

  • Harrison, G. W. 1979. “Global Stability of Good Chains.”Am. Nat. 114, 455–457.

    Article  MathSciNet  Google Scholar 

  • May, R. M. 1973. “Mass and Energy Flow in Closed Ecosystems: a Comment.”J. theor. Biol. 39, 155–163.

    Article  Google Scholar 

  • Nisbet, R. M. and W. S. C. Gurney. 1976. “Model of Material Cycling in a Closed Ecosystem.”Nature 264, 633–634.

    Article  Google Scholar 

  • —, J. McKinstry and W. S. C. Gurney. 1983. “A ‘Strategic’ model of Material Cycling in a Closed Ecosystem”Mathl Biosci. 64, 99–113.

    Article  MATH  Google Scholar 

  • Robinson, J. V. and W. D. Valentine. 1979. “The Concept of Elasticity. Invulnerability and Invadability.”J. theor. Biol. 81, 91–104.

    Article  Google Scholar 

  • — and G. S. Ladde. 1982. “Feasibility Constraints on the Elastic Expansion of Ecosystem Models.”J. theor. Biol. 92, 277–287.

    Article  MathSciNet  Google Scholar 

  • Solimano, F. and E. Beretta. 1982 “Graph Theoretical Criteria for Stability and Boundedness of Predator-Prey System.”Bull. math. Biol. 44, 579–586.

    Article  MATH  MathSciNet  Google Scholar 

  • Ulanowicz, R. E. 1972. “Mass and energy Flow in Closed Ecosystems.”J. theor. Biol. 34, 239–253.

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Jadavpur University, 700032, Calcutta, India

    A. B. Roy

  2. Istituto di Biomatematica, Università di Urbino, I-61029, Urbino, Italy

    F. Solimano

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  1. A. B. Roy
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  2. F. Solimano
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Roy, A.B., Solimano, F. Global stability of partially closed food-chains with resources. Bltn Mathcal Biology 48, 455–468 (1986). https://doi.org/10.1007/BF02462317

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  • DOI: https://doi.org/10.1007/BF02462317

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