Skip to main content
SpringerLink
Log in

A necessary and sufficient condition for the existence of chaotic dynamics in a neoclassical growth model with a pollution effect

  • Research Article
  • Published:
Economic Theory Bulletin Aims and scope Submit manuscript

Abstract

In this paper, we study a neoclassical growth model with a (productivity inhibiting) pollution effect. In particular, we obtain a necessary and sufficient condition for the existence of a topological chaos. We investigate how the condition changes as the strength of the pollution effect changes. This is a new application of a recent result characterising the existence of a topological chaos for a unimodal interval map by Deng et al. (J Econ Theory 201:Article 105446, 2022).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Data availability

All programming files (Jupyter notebooks) used for numerical computations or to generate plots in this paper are available upon request.

References

  • Block, L.S., Coppel, W.A.: Dynamics in One Dimension. Springer, Berlin (1992)

    Book  Google Scholar 

  • Day, R.H.: Irregular growth cycles. Am. Econ. Rev 72, 406–414 (1982)

    Google Scholar 

  • Deng, L., Khan, M.A., Mitra, T.: Continuous unimodal maps in economic dynamics: on easily verifiable conditions for topological chaos. J. Econ. Theory 201, Article 105446 (2022)

    Article  Google Scholar 

  • Ruette, S.: Chaos on the Interval. American Mathematical Society, Providence (2017)

    Book  Google Scholar 

  • Solow, R.M.: Contribution to the theory of economic growth. Q. J. Econ. 70, 65–94 (1956)

    Article  Google Scholar 

  • Yorke, J.A., Yorke, E.: Chaotic behavior and fluid dynamics. In Swinney, H.L., Gollub, J.P. (eds.) Hydrodynamic Instabilities and the Transition to Turbulence (1985)

Download references

Author information

Authors and Affiliations

  1. Faculty of International Liberal Arts, Soka University, 1-236, Tangi-machi, Hachioji-shi, Tokyo, 192-8577, Japan

    Tomohiro Uchiyama

Authors
  1. Tomohiro Uchiyama
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tomohiro Uchiyama.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Uchiyama, T. A necessary and sufficient condition for the existence of chaotic dynamics in a neoclassical growth model with a pollution effect. Econ Theory Bull (2024). https://doi.org/10.1007/s40505-024-00264-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s40505-024-00264-y

Keywords

Search

Navigation