Periodic, Aperiodic, and Stochastic Behavior of Differential-Difference Equations Modeling Biological and Economical Processes

  • U. an der Heiden
Part of the International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique book series (ISNM, volume 62)


In this paper we consider the behavior of solutions to the differential-difference equation
$$dx(t)/dt = a\{ f(x(t - 1)) - x(t)\} ,$$
where f: ℝ → ℝ is a piecewise continuous function and a ∈ ℝ, a >O. Such equations have found several applications in biology and economics. E.g. they concern the regulation of red blood cell populations [13], [17], excitatory-inhibitory neural interactions [2], [4], [5], regulation of enzyme synthesis [4], respiratory control circuits [12], and modeling of commodity cycles [1].


Periodic Solution Unique Fixed Point Symbolic Dynamic Stochastic Behavior Homoclinic Solution 
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Copyright information

© Springer Basel AG 1983

Authors and Affiliations

  • U. an der Heiden
    • 1
  1. 1.Research Center “Stability Limits of Biological Systems”Universität Bremen, NW2Bremen 33W.Germany

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