Dynamics of a multiplier–accelerator model with nonlinear investment function

A. K. Naimzada, Nicolo' Pecora

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7 Citations (Scopus)


In this paper, we show how a rich variety of dynamics may arise in a simple multiplier–accelerator model when a nonlinearity is introduced in the investment function. A specific sigmoidal functional form is used to model investments with respect to the variation in national income, in order to bound the level of investments. In fact, due to obvious material constraints, business strategies cannot sustain infinite investments. With the aid of analytical and numerical tools, we investigate the stability conditions, bifurcations, as well as periodic and chaotic dynamics for different specifications of the model that may include or not an endogenous government expenditure. We obtain some comparative statics results that shed light on the stabilizing or destabilizing role of the various parameters in the model. Globally, we study multistability phenomena, i.e., the coexistence of different kinds of attractors with a rich and complex dynamic structure.
Original languageEnglish
Pages (from-to)1147-1161
Number of pages15
JournalNonlinear Dynamics
Publication statusPublished - 2016


  • Aerospace Engineering
  • Applied Mathematics
  • Bifurcations
  • Business cycle
  • Control and Systems Engineering
  • Electrical and Electronic Engineering
  • Global analysis
  • Mechanical Engineering
  • Nonlinear dynamics
  • Ocean Engineering
  • Stability


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