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  • 1
    Electronic Resource
    Electronic Resource
    On manifolds of equilibria in the selection model for multiple alleles (1975)
    Springer
    Journal of mathematical biology 1 (1975), S. 321-330 
    Details
    ISSN: 1432-1416
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Summary A population subjected to the Fisher-Wright-Haldane selection model for three alleles always converges to a fixed state even if the matrix of viabilities is singular. In this case there can occur lines of equilibrium points being partly attracting, partly repulsive. If there are n alleles then the manifolds of equilibrium points can be of every dimension between zero and n−1. Some criteria for such manifolds to be asymptotically stable are derived in terms of determinants and eigenvalues of the viability matrix.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00279851
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Nonhomogeneous spatial distributions of populations (1975)
    Springer
    Journal of mathematical biology 2 (1975), S. 165-176 
    Details
    ISSN: 1432-1416
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Summary Spatial inhomogeneities such as nonconstant population densities usually will be attributed to random effects or to an inhomogeneous substrate. Such an explanation may be incorrect since from certain chemical reactions it is known that the interaction of species together with diffusion may generate nonhomogeneous spatial structures. However, the effect of boundary conditions has been so far neglected. In this paper nonlinear and linear interaction-diffusion models are investigated under various side-conditions by analytic methods and by computer simulations. A remarkable fact, as compared with earlier results in the field, is the example of an interaction-diffusion process which in the whole space has only the constant as a stable limit distribution, whereas the introduction of a side condition, e.g. a population reservoir or a barrier, leads to standing spatial population waves.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00275801
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Delays in physiological systems (1979)
    Springer
    Journal of mathematical biology 8 (1979), S. 345-364 
    Details
    ISSN: 1432-1416
    Keywords: Differential-Difference equations ; Delays ; Biochemical reactions ; Lateral inhibition ; Entire functions ; Periodic and chaoticoscillations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Summary In comparison to most physical or chemical systems, biological systems are of extreme complexity. In addition the time needed for transport or processing of chemical components or signals may be of considerable length. Thus temporal delays have to be incorporated into models leading to differential-difference and functional differential equations rather than ordinary differential equations. A number of examples, on different levels of biological organization, demonstrate that delays can have an influence on the qualitative behavior of biological systems: The existence or non-existence of instabilities and periodic or even chaotic oscillations can entirely depend on the presence or absence of delays with appropriate duration.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00275831
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Existence of periodic solutions of a nerve equation (1976)
    Springer
    Biological cybernetics 21 (1976), S. 37-39 
    Details
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract A recently developed continuous neuronal model is transformed into a system which is closely related to the theory of cellular control processes. In a broad region of parameter values periodic solutions of the equations describing the neuron do exist.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00326671
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    Generation of the nervous impulse and periodic oscillations (1976)
    Springer
    Biological cybernetics 23 (1976), S. 211-218 
    Details
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract Usually the models for the excitation and propagation of the nervous impulse are studied either in the space-clamp situation or on a model axon extended on both sides to infinity. Following Fitzhugh in the present paper the release of an impulse train at the axon hillock is studied within the scope of Fitzhugh's BVP model. The existence and stability of periodic oscillations are studied by direct methods, also the relation to Liénard's equation. The exact correspondence between the BVP model and the socalled Nagumo-equation is established. For typical examples the solutions are computed by numerical methods.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00340337
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    Paper (German National Licenses)
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