Some reflections on past and future of nonlinear dynamics in economics and finance

  • Mikhail Anufriev
  • Davide Radi
  • Fabio Tramontana


This paper offers an overview of the literature on the economic and financial applications of theory of nonlinear dynamics, especially bifurcation theory. After a short introductory discussion of the first nonlinear dynamic models in social sciences and the economic relevance of the zoo of bifurcations and complicated dynamics that such models can generate, we present an overview of the literature on nonlinear dynamic models in the areas of underdevelopment, environmental poverty traps, the management of common goods, industrial organization and financial markets. The review of the literature is enriched by reflections and ideas for future research.


Nonlinear systems Bifurcation theory Complex phenomena in economics and finance Models of bounded rationality and information Heterogeneous agents 

Mathematics Subject Classification

C02 D40 G12 L13 O10 O40 Q50 



The authors are very grateful to Gian Italo Bischi, Mauro Sodini and two reviewers for their careful and meticulous reading of the paper. Very special thanks go to the organizers, speakers and participants of the XLI AMASES Annual Meeting in Cagliari (2017). Davide Radi acknowledges financial support from VŠB-TU Ostrava under the SGS Project SP2018/34. Mikhail Anufriev acknowledges financial support from the Australian Research Council through Discovery Project DP140103501.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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© Associazione per la Matematica Applicata alle Scienze Economiche e Sociali (AMASES) 2018

Authors and Affiliations

  1. 1.Department of EconomicsUniversity of Technology SydneySydneyAustralia
  2. 2.Department of Economics and ManagementUniversity of PisaPisaItaly
  3. 3.Department of Finance, Faculty of EconomicsVS̆B–Technical University of OstravaOstravaCzech Republic
  4. 4.Department of Mathematical SciencesCatholic University of the Sacred HeartMilanItaly

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