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  • Abiotic resource  (1)
  • Boundedness  (1)
  • Chemostat equations  (1)
  • 1
    Electronic Resource
    Electronic Resource
    Oscillations in a system with material cycling (1988)
    Springer
    Journal of mathematical biology 26 (1988), S. 143-167 
    Details
    ISSN: 1432-1416
    Keywords: Biotic species ; Abiotic resource ; Time delay ; Stability ; Hopf bifurcation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We study a system of two integrodifierential equations which models the evolution of a biotic species feeding on an abiotic resource. We also consider nutrient recycling with time delay. By Hopf bifurcation theory we prove the existence of stable oscillations for a range of values of the input of nutrients.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00277730
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  • 2
    Electronic Resource
    Electronic Resource
    Stability in chemostat equations with delayed nutrient recycling (1990)
    Springer
    Journal of mathematical biology 28 (1990), S. 99-111 
    Details
    ISSN: 1432-1416
    Keywords: Chemostat equations ; Recycling ; Time lags ; Stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The growth of a species feeding on a limiting nutrient supplied at a constant rate is modelled by chemostat-type equations with a general nutrient uptake function and delayed nutrient recycling. Conditions for boundedness of the solutions and the existence of non-negative equilibria are given for the integrodifferential equations with distributed time lags. When the time lags are neglected conditions for the global stability of the positive equilibrium and for the extinction of the species are provided. The positive equilibrium continues to be locally stable when the time lag in recycling is considered and this is proved for a wide class of memory functions. Computer simulations suggest that even in this case the region of stability is very large, but the solutions tend to the equilibrium through oscillations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00171521
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  • 3
    Electronic Resource
    Electronic Resource
    Global stability and oscillations in classical Lotka-Volterra loops (1987)
    Springer
    Journal of mathematical biology 24 (1987), S. 603-616 
    Details
    ISSN: 1432-1416
    Keywords: Predator-prey system ; Loop ; Stability ; Boundedness ; Oscillations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The paper considers the classical Volterra system of n (⩾ 3) species in predator-prey relation forming a loop, and derives some global properties of its solutions. Sufficient conditions for global asymptotic stability in terms of parameters are obtained, and also the region of global boundedness in the parameter space is indicated. Lastly a three species system is discussed in detail in relation to its global stability, unboundedness of solutions, existence of periodic and non-periodic oscillations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00275505
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