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  • 1
    Electronic Resource
    Electronic Resource
    Feedback and delays in neurological diseases: A modeling study using gynamical systems (1993)
    Springer
    Bulletin of mathematical biology 55 (1993), S. 525-541 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Numerous regulatory mechanisms in motor control involve the presence of time delays in the controlled behavior of the system. Experimentally, we have shown that an increase of the time delay in visual feedback induces different oscillations in control subjects and in patients with neurological diseases during the performance of a simple compensatory tracking task. A preliminary model is proposed to describe the oscillations observed in control subjects and in patients with neurological diseases. The influence of delays in two feedback loops are the main components of the motor control circuitry involved in this task and are studied from an analytical and physiological perspective. We analytically determine the influence in the model of each of these delays on the stability of the finger position. In addition, the influence of stochastic elements (“noise”) in the modeling equation is seen to contribute qualitatively to a more accurate reproduction of experimental traces in patients with Parkinson's disease but not in patients with cerebellar disease.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460649
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  • 2
    Electronic Resource
    Electronic Resource
    Complex dynamics and multistability in a damped harmonic oscillator with delayed negative feedback (1995)
    Woodbury, NY : American Institute of Physics (AIP)
    Chaos 5 (1995), S. 640-645 
    Details
    ISSN: 1089-7682
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A center manifold reduction and numerical calculations are used to demonstrate the presence of limit cycles, two-tori, and multistability in the damped harmonic oscillator with delayed negative feedback. This model is the prototype of a mechanical system operating with delayed feedback. Complex dynamics are thus seen to arise in very plausible and commonly occurring mechanical and neuromechanical feedback systems. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.166134
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  • 3
    Electronic Resource
    Electronic Resource
    Dynamical disease: Identification, temporal aspects and treatment strategies of human illness (1995)
    Woodbury, NY : American Institute of Physics (AIP)
    Chaos 5 (1995), S. 1-7 
    Details
    ISSN: 1089-7682
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Dynamical diseases are characterized by sudden changes in the qualitative dynamics of physiological processes, leading to abnormal dynamics and disease. Thus, there is a natural matching between the mathematical field of nonlinear dynamics and medicine. This paper summarizes advances in the study of dynamical disease with emphasis on a NATO Advanced Research Worshop held in Mont Tremblant, Québec, Canada in February 1994. We describe the international effort currently underway to identify dynamical diseases and to study these diseases from a perspective of nonlinear dynamics. Linear and nonlinear time series analysis combined with analysis of bifurcations in dynamics are being used to help understand mechanisms of pathological rhythms and offer the promise for better diagnostic and therapeutic techniques. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.166069
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  • 4
    Electronic Resource
    Electronic Resource
    A Model for the Regulation of Mammalian Platelet Production (1987)
    Oxford, UK : Blackwell Publishing Ltd
    Annals of the New York Academy of Sciences 504 (1987), S. 0 
    Details
    ISSN: 1749-6632
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Natural Sciences in General
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1749-6632.1987.tb48740.x
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  • 5
    Electronic Resource
    Electronic Resource
    Book reviews (1992)
    Springer
    Bulletin of mathematical biology 54 (1992), S. 895-901 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459935
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  • 6
    Electronic Resource
    Electronic Resource
    Book reviews (1988)
    Springer
    Bulletin of mathematical biology 50 (1988), S. 313-328 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02458885
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  • 7
    Electronic Resource
    Electronic Resource
    Limit cycles, tori, and complex dynamics in a second-order differential equation with delayed negative feedback (1995)
    Springer
    Journal of dynamics and differential equations 7 (1995), S. 213-236 
    Details
    ISSN: 1572-9222
    Keywords: Time delay ; negative feedback ; Hopf bifurcations ; center manifold ; invariant tori ; 34K15 ; 54F36 ; 93D15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We analyze a second-order, nonlinear delay-differential equation with negative feedback. The characteristic equation for the linear stability of the equilibrium is completely solved, as a function of two parameters describing the strength of the feedback and the damping in the autonomous system. The bifurcations occurring as the linear stability is lost are investigated by the construction of a center manifold: The nature of Hopf bifurcations and more degenerate, higher-codimension bifurcations are explicitly determined.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02218819
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  • 8
    Electronic Resource
    Electronic Resource
    Stability in a model of a delayed neural network (1993)
    Springer
    Journal of dynamics and differential equations 5 (1993), S. 607-623 
    Details
    ISSN: 1572-9222
    Keywords: Neural networks ; time delays ; oscillations ; 34K15 ; 34K20 ; 92B20
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The stability of the null solution in a system of coupled cells is investigated. Each cell evolves according to Hopfield's equation for an analog circuit, with a delay incorporated to account for finite switching speed of amplifiers. A necessary and sufficient condition on the connection matrix is obtained for delay-induced oscillations to be possible in a general (not necessarily symmetric) network.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01049141
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  • 9
    Electronic Resource
    Electronic Resource
    Consumer memory and price fluctuations in commodity markets: An integrodifferential model (1989)
    Springer
    Journal of dynamics and differential equations 1 (1989), S. 299-325 
    Details
    ISSN: 1572-9222
    Keywords: Commodity markets ; time delays ; stability ; Hopf bifurcation ; 34K15 ; 45J05 ; 90A16
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A model for the dynamics of price adjustment in a single commodity market is developed. Nonlinearities in both supply and demand functions are considered explicitly, as are delays due to production lags and storage policies, to yield a nonlinear integrodifferential equation. Conditions for the local stability of the equilibrium price are derived in terms of the elasticities of supply and demand, the supply and demand relaxation times, and the equilibrium production-storage delay. The destabilizing effect of consumer memory on the equilibrium price is analyzed, and the ensuing Hopf bifurcations are described.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01053930
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  • 10
    Electronic Resource
    Electronic Resource
    Periodic pulsatile stimulation of a nonlinear oscillator (1986)
    Springer
    Journal of mathematical biology 24 (1986), S. 217-232 
    Details
    ISSN: 1432-1416
    Keywords: Biological oscillator ; Maps of the circle ; Entrainment
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We consider pulsatile periodic stimulation of an integrate-and-fire oscillator, and investigate the possible phase-locked patterns between the intrinsic rhythm and the forcing system. These stimulations are varied according to their period and intensity, corresponding to controllable experimental parameters. Phase transition curves are derived and analyzed under functional iteration. Two different perturbative mechanisms are considered, leading to significant differences in possible behaviors. Bistability can be obtained in one case. The analysis is reduced to the investigation of two-parameter families of discontinuous maps of the circle into itself.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00276000
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