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  • 1
    Electronic Resource
    Electronic Resource
    Eye movements and the enhancement of edges (1985)
    Springer
    Journal of mathematical biology 21 (1985), S. 273-283 
    Details
    ISSN: 1432-1416
    Keywords: Eye movements ; edge enhancement ; mach bands
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A mathematical examination of retinal photochemistry leads to a hypothesis for Mach band phenomena based on eye movements. This retinal model suggests why minimally distinct borders fade under eye fixation and agrees qualitatively with subjective measures of border contrast as a function of overall field luminance.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00276226
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    The nature of the coupling between segmental oscillators of the lamprey spinal generator for locomotion: A mathematical model (1982)
    Springer
    Journal of mathematical biology 13 (1982), S. 345-369 
    Details
    ISSN: 1432-1416
    Keywords: Locomotion ; Pattern generator ; Dynamical systems ; Oscillators
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We present a theoretical model which is used to explain the intersegmental coordination of the neural networks responsible for generating locomotion in the isolated spinal cord of lamprey. A simplified mathematical model of a limit cycle oscillator is presented which consists of only a single dependent variable, the phase θ(t). By coupling N such oscillators together we are able to generate stable phase locked motions which correspond to traveling waves in the spinal cord, thus simulating “fictive swimming”. We are also able to generate irregular “drifting” motions which are compared to the experimental data obtained from cords with selective surgical lesions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00276069
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Chaos in a system with a periodically disappearing separatrix (1990)
    Springer
    Nonlinear dynamics 1 (1990), S. 401-420 
    Details
    ISSN: 1573-269X
    Keywords: Chaos ; perturbation methods ; elliptic functions ; differential equations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We investigate the system $$\ddot x - x\cos \varepsilon 1 + x^3 = 0$$ in which ε≪1 by using averaging and elliptie functions. It is shown that this system is applicable to the dynamics of the familiar rotating-plane pendulum. The slow foreing permits us to envision an ‘instantancous phase portrait’ in the $$x - \dot x$$ phase plane which exhibits a center at the origin when cos ε1≤0 and a saddle and associated double homoclinic loop separatrix when cos ɛ 1 〉 0. The chaos in this problem is related to the question of on which side (left (=L) or right (=R)) of the reappearing double homoclinic loop separatrix a motion finds itself. We show that the sequence of L's and R's exhibits sensitive dependence on initial conditions by using a simplified model which assumes that motions cross the instantancous separatrix instantancously. We also present an improved model which ‘patches’ a separatrix boundary layer onto the averaging model. The predictions of both models are compared with the results of numerical integration.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01893171
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    Paper (German National Licenses)
    Fulltext
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