Operations-Research-Spektrum

, Volume 16, Issue 2, pp 101–111 | Cite as

Complex dynamics in a threshold advertising model

  • Gustav Feichtinger
  • Cars H. Hommes
  • Alexandra Milik
Article

Abstract

During the last decade economic models of varying complexity have been studied by using the qualitative theory of nonlinear dynamical systems theory. The purpose of the present paper is to analyze an economic model which is as simple as possible but exhibits sufficient nonlinearity to admit chaotic orbits. A firm's market share is assumed to be influenced only by a simple threshold advertising rule. It turns out that such a simple rule may create complex behavioural patterns, i.e., periodic orbits of any length and even chaotic, seemingly unpredictable time paths. By using the package LOCBIF we are able to investigate for which model parameters chaos arises and how the transition from stable equilibrium to chaos occurs.

Key words

Advertising model nonlinear dynamics chaos threshold rule marketing 

Zusammenfassung

Im Laufe des letzten Jahrzehnts wurden mit Hilfe der Theorie nichtlinearer dynamischer Systeme ökonomische Modelle unterschiedlicher Komplexität untersucht. Der Zweck der vorliegenden Arbeit ist es, ein Model zu analysieren, das so einfach wie möglich ist, aber genügend Nichtlinearität aufweist, um chaotische Orbits zu ermöglichen. Es wird angenommen, daß der Marktanteil eines Unternehmens nur von einer einfachen „Alles oder Nichts“-Werbestrategie beeinflußt wird. Es stellt sich heraus, daß eine derart einfache Strategie komplexes Verhalten erzeugen kann, d. h. periodische Orbits jeder Länge und sogar chaotische, scheinbar zufällige Zeitpfade. Mit Hilfe des Progammpakets LOCBIF sind wir in der Lage zu untersuchen, für welche Parameter Chaos entsteht und wie der Übergang von einem stabilen Gleichgewicht zu Chaos erfolgt.

Schlüsselwörter

Werbemodell nichtlineare Dynamik Chaos Schwellenregel Marketing 

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Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • Gustav Feichtinger
    • 1
  • Cars H. Hommes
    • 1
  • Alexandra Milik
    • 1
  1. 1.Institut für Ökonometrie, Operations Research und SystemtheorieTechnische Universität WienWienAustria

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