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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)

Abstract

In this paper we consider the behavior of solutions to the differential-difference equation
$$dx(t)/dt = a\{ f(x(t - 1)) - x(t)\} ,$$
(1.1)
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].

Keywords

Periodic Solution Unique Fixed Point Symbolic Dynamic Stochastic Behavior Homoclinic Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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