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  • Dynamical systems  (1)
  • Smale horseshoe  (1)
  • piecewise linear map  (1)
  • 1
    Digitale Medien
    Digitale Medien
    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
    Schlagwort(e): Locomotion ; Pattern generator ; Dynamical systems ; Oscillators
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00276069
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 2
    Digitale Medien
    Digitale Medien
    Chaos in a mapping describing elastoplastic oscillations (1995)
    Springer
    Nonlinear dynamics 8 (1995), S. 111-139 
    Details
    ISSN: 1573-269X
    Schlagwort(e): Elastoplastic oscillator ; piecewise linear map ; chaos ; Smale horseshoe ; symbolic dynamics
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00045009
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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