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  • Articles  (4)
  • stability
  • Springer  (4)
  • 1980-1984  (4)
  • 1984  (4)
  • Mathematics  (3)
  • Biology  (3)
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  • Articles  (4)
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  • Springer  (4)
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  • 1980-1984  (4)
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  • 1
    Electronic Resource
    Electronic Resource
    Existence and stability of equilibria in age-structured population dynamics (1984)
    Springer
    Journal of mathematical biology 20 (1984), S. 259-276 
    Details
    ISSN: 1432-1416
    Keywords: Age-structured population dynamics ; equilibria ; stability ; bifurcation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The existence of positive equilibrium solutions of the McKendrick equations for the dynamics of an age-structured population is studied as a bifurcation phenomenon using the inherent net reproductive rate n as a bifurcation parameter. The local existence and uniqueness of a branch of positive equilibria which bifurcates from the trivial (identically zero) solution at the critical value n=1 are proved by implicit function techniques under very mild smoothness conditions on the death and fertility rates as functional of age and population density. This first requires the development of a suitable linear theory. The lowest order terms in the Liapunov-Schmidt expansions are also calculated. This local analysis supplements earlier global bifurcation results of the author. The stability of both the trivial and the positive branch equilibria is studied by means of the principle of linearized stability. It is shown that in general the trivial solution losses stability as n increases through one while the stability of the branch solution is stable if and only if the bifurcation is supercritical. Thus the McKendrick equations exhibit, in the latter case, a standard exchange of stability with regard to equilibrium states as they depend on the inherent net reproductive rate. The derived lower order terms in the Liapunov-Schmidt expansions yield formulas which explicitly relate the direction of bifurcation to properties of the age-specific death and fertility rates as functionals of population density. Analytical and numerical results for some examples are given which illustrate these results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00275988
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  • 2
    Electronic Resource
    Electronic Resource
    Predator-prey relationships: Indiscriminate predation (1984)
    Springer
    Journal of mathematical biology 21 (1984), S. 25-34 
    Details
    ISSN: 1432-1416
    Keywords: Predator-prey ; density dependence ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The Gurtin and Levine model5 is studied in this paper under the assumption that the fecundity of prey depends on age as well as on the total population sizes of prey and predators. The purpose of this study is to see the effect of this density dependence on the stability criteria for the equilibria of the model equations. It is shown that there are cases when, due to density dependence, the model which is originally neutrally stable becomes stable.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00275220
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  • 3
    Electronic Resource
    Electronic Resource
    The response of a harpacticoid copepod community to sediment disturbance in a semi-enclosed lagoon (1984)
    Springer
    Hydrobiologia 118 (1984), S. 127-133 
    Details
    ISSN: 1573-5117
    Keywords: meiofauna ; Harpacticoida ; eutrophication ; stability ; colonisation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract The harpacticoid fauna of a sandy sediment in the Sluice Dock of Ostend, Belgium, was dominated by a single species, Canuella perplexa, that attained an average annual density of over 400 ind. 10 cm−2 in 1976 and 1977, whereas other species had a total mean density of less than 10 ind. 10 cm−2. In the summer of 1979 a dystrophic crisis with abundant growth of Ulva occurred and in March 1980 the lagoon was drained. After refilling of the lagoon, the sediment was immediately colonized by good swimming harpacticoids, that attained densities of 200 ind. 10 cm−2. Three months after refilling Canuella perplexa reappeared and the system returned to its original state within one month.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00031795
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  • 4
    Electronic Resource
    Electronic Resource
    Stochastic scheduling problems I — General strategies (1984)
    Springer
    Mathematical methods of operations research 28 (1984), S. 193-260 
    Details
    ISSN: 1432-5217
    Keywords: Analytic behaviour of strategies ; continuous strategies ; ES strategies ; MES strategies ; machine idleness ; monotonicity behaviour ; optimal strategies ; preselectivity ; regular measure of performance ; scheduling problems ; stability ; stochastic dynamic optimization ; stochastically ordered distributions ; stochastic scheduling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract The paper contains an introduction to recent developments in the theory of non-preemptive stochastic scheduling problems. The topics covered are: arbitrary joint distributions of activity durations, arbitrary regular measures of performance and arbitrary precedence and resource constraints. The possible instability of the problem is demonstrated and hints are given on stable classes of strategies available, including the combinatorial vs. analytical characterization of such classes. Given this background, the main emphasis of the paper is on the monotonicity behaviour of the model and on the existence of optimal strategies. Existing results are presented and generalized, in particular w.r.t. the cases of lower semicontinuous performance measures or joint duration distributions having a Lebesgue density.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01919323
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