Persistent oscillations in a threshold adjustment model

Abstract

In this paper we present a simple time-continuous behavioural model of habit formation. Addictive behaviour is damped by a threshold which adapts itself to the habit. This adaptive behaviour of the threshold may lead to periodic fluctuations of the consumption rate, the habit and the threshold. It turns out that both a low adjustment rate of the threshold as well as a steep consumption function favour oscillatory patterns.

Keywords:

• Addiction
• Habit formation
• Limit cycles
• Nonlinear dynamical systems
• Threshold models