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  • Biochemical reactions  (1)
  • Nonlinear differential equations of second order with deviating argument  (1)
Document type
Keywords
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Years
  • 1
    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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  • 2
    Electronic Resource
    Electronic Resource
    Oscillatory modes in a nonlinear second-order differential equation with delay (1990)
    Springer
    Journal of dynamics and differential equations 2 (1990), S. 423-449 
    Details
    ISSN: 1572-9222
    Keywords: Nonlinear differential equations of second order with deviating argument ; oscillations ; periodic solutions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Solution properties of the nonlinear second-order delay-differential equation x(t)=−ax(t)+f[x(t−Τ)] are studied wheref is a piecewise constant function which mimics negative feedback. We show that the solutions can be obtained by a simple geometrical construction which, in principle, can be implemented using a ruler and a compass. Analytical results guarantee the existence and stability properties of limit cycle solutions. Computer-aided constructions reveal a remarkable richness of different types of dynamical behaviors including a variety of unconventional bifurcation schemes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01054042
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    Paper (German National Licenses)
    Fulltext
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