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  • Articles: DFG German National Licenses  (2)
  • Dynamical systems  (1)
  • piecewise linear map  (1)
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  • Articles: DFG German National Licenses  (2)
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  • 1
    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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  • 2
    Electronic Resource
    Electronic Resource
    Chaos in a mapping describing elastoplastic oscillations (1995)
    Springer
    Nonlinear dynamics 8 (1995), S. 111-139 
    Details
    ISSN: 1573-269X
    Keywords: Elastoplastic oscillator ; piecewise linear map ; chaos ; Smale horseshoe ; symbolic dynamics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We study the local and global dynamical behavior of a two dimensional piecewise linear map which describes the asymptotic motions of a single degree of freedom, parametrically excited, elastoplastic oscillator after it has settled down to purely elastic oscillations. We give existence and stability conditions for periodic orbits and prove that chaos, in the form of a Smale horseshoe, exists at specific, but representative, parameter values. We interpret simulations of the elastoplastic oscillator itself in the light of these results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00045009
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    Paper (German National Licenses)
    Fulltext
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