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  • Articles  (6)
  • Articles: DFG German National Licenses  (6)
  • Stability  (6)
  • 2010-2014
  • 1980-1984  (6)
  • 1950-1954
  • 1980  (6)
  • Mathematics  (6)
  • History
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  • Articles  (6)
Source
  • Articles: DFG German National Licenses  (6)
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  • 2010-2014
  • 1980-1984  (6)
  • 1950-1954
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  • 1
    Electronic Resource
    Electronic Resource
    Lotka-Volterra equations: Decomposition, stability, and structure (1980)
    Springer
    Journal of mathematical biology 9 (1980), S. 65-83 
    Details
    ISSN: 1432-1416
    Keywords: Nonnegative equilibria ; Stability ; Decompositions ; Sub-communities ; Structural perturbations ; Connective stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Summary The major objective of this paper is to propose a new decomposition-aggregation framework for stability analysis of Lotka-Volterra equations employing the concept of vector Liapunov functions. Both the disjoint and the overlapping decompositions are introduced to increase flexibility in constructing Liapunov functions for the overall system. Our second objective is to consider the Lotka-Volterra equations under structural perturbations, and derive conditions under which a positive equilibrium is connectively stable. Both objectives of this paper are directed towards a better understanding of the intricate interplay between stability and complexity in the context of robustness of model ecosystems represented by Lotka-Volterra equations. Only stability of equilibria in models with constant parameters is considered here. Nonequilibrium analysis of models with nonlinear time-varying parameters is the subject of a companion paper.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00276036
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  • 2
    Electronic Resource
    Electronic Resource
    Effects of mean current and shear on stability of depth distributions of marine phytoplankton (1980)
    Springer
    Journal of mathematical biology 10 (1980), S. 33-51 
    Details
    ISSN: 1432-1416
    Keywords: Plankton ; Stability ; Perturbations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Linear perturbation theory is used to examine the stability of steady-state distributions of marine phytoplankton in the presence of a mean current with shear. Solutions are obtained for the general initial-value problem and it is found that all distributions are asymptotically stable so long as the rate of shear is greater than the local production. On the other hand, the early time behavior indicates that the system can be altered, if accomplished soon enough, depending upon a relative combination of diffusion, advection and production. Quantitative assessments are made where data are available.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00276394
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Persistence of predator-prey systems in an uncertain environment (1980)
    Springer
    Journal of mathematical biology 10 (1980), S. 65-77 
    Details
    ISSN: 1432-1416
    Keywords: Predator-prey ; Persistence ; Stability ; Differential inequalities
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Summary The time derivatives of prey and predator populations are assumed to satisfy a set of inequalities, instead of a precise differential equation, reflecting an uncertain environmental and/or lack of knowledge by the modeler. A system of differential equations is found whose solution gives the boundary of a persistent set, which is positive flow invariant for any system satisfying the inequalities. Conditions are given for the persistent set to be bounded away from both axes, which show that resonance effects cannot drive either predator or prey to extinction if that does not happen for an autonomous system satisfying the inequalities. In general predator-prey systems are more persistent when there is strong asymptotic stability, when there is correlation between prey and predator dynamics, when the effect of perturbations is density dependent, and are more persistent under perturbations of the prey than of the predator.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00276396
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  • 4
    Electronic Resource
    Electronic Resource
    One-dimensional λ-ω target patterns: Empirical stability tests (1980)
    Springer
    Journal of mathematical biology 10 (1980), S. 97-100 
    Details
    ISSN: 1432-1416
    Keywords: Reaction diffusion equations ; Wave-trains ; Stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Summary Stability of a class of solutions to reaction-diffusion equations is studied numerically. It is found that the solutions do not persist under a variety of boundary conditions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00276399
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  • 5
    Electronic Resource
    Electronic Resource
    Integral equation models for endemic infectious diseases (1980)
    Springer
    Journal of mathematical biology 9 (1980), S. 37-47 
    Details
    ISSN: 1432-1416
    Keywords: Epidemiology ; Endemic infectious diseases ; Deterministic models ; Thresholds ; Distributed delays ; Stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Summary Endemic infectious diseases for which infection confers permanent immunity are described by a system of nonlinear Volterra integral equations of convolution type. These constant-parameter models include vital dynamics (births and deaths), immunization and distributed infectious period. The models are shown to be well posed, the threshold criteria are determined and the asymptotic behavior is analysed. It is concluded that distributed delays do not change the thresholds and the asymptotic behaviors of the models.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00276034
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  • 6
    Electronic Resource
    Electronic Resource
    The existence of globally stable equilibria of ecosystems of the generalized Volterra type (1980)
    Springer
    Journal of mathematical biology 10 (1980), S. 401-415 
    Details
    ISSN: 1432-1416
    Keywords: Stability ; Volterra ecosystems ; Linear complementarity theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In this paper, global asymptotic stability of ecosystems of the generalized Volterra type $$dx_i /dt = x_i \left( {b_{i - } \mathop \sum \limits_{j = 1}^n a_{ij} x_j } \right),{\text{ }}i = 1,...,n,$$ is investigated. We obtain the conditions for the existence of a nonnegative and stable equilibrium point of the system by applying a result of linear complementarity theory. The results of this paper show that there exists a class of systems that do not have multiple domains of attractions. This class is defined in terms of the species interactions alone, and does not involve carrying capacities or species net birth rates.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00276098
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