Skip to main content

Modeling Limits to Growth

  • Chapter
  • First Online:
System Dynamics Modeling with R

Part of the book series: Lecture Notes in Social Networks ((LNSN))

  • 4518 Accesses


This chapter introduces system dynamics models of limits to growth. First, a one-stock model is presented, where the growth rate varies, and is influenced by the system’s carrying capacity. Second, a model of economic growth is described, which captures the law of diminishing returns, a feature of many economic systems. Third, a two-stock model of limits to growth is specified, where a growing stock consumes its carrying capacity, and this dynamic leads to growth followed by rapid decline. Before introducing the limits to growth models, an explanation of an important formulation method in system dynamics is presented. This allows modelers to construct robust equations to model the effect of one variable on another. This is useful for many system dynamics models, particularly where one system stock influences another system stock.

There will always be limits to growth. They can be self-imposed.

If they aren’t, they will be system-imposed.

Donella H. Meadows, Thinking in Systems: A Primer (2008, p. 103).

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

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
USD 89.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 119.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 119.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions


  • Bacaër N (2011) Verhulst and the logistic equation (1838). In: A short history of mathematical population dynamics. Springer London, pp 35–39

    Google Scholar 

  • Meadows DH (2008) Thinking in systems: a primer. Chelsea Green Publishing

    Google Scholar 

  • Page S (2015) A model of growth. Supporting material for Coursera Model Thinking MOOC Course. Accessed 30 June 2015

  • Richardson GP (1991) Feedback thought in social science and systems theory. Pegasus Communications, Inc., Chicago

    Google Scholar 

  • Solow RM (1956) A contribution to the theory of economic growth. Quart J Econ 70:65–94

    Google Scholar 

  • Sterman JD (2000) Business dynamics: systems thinking and modeling for a complex world. Irwin/McGraw-Hill, Boston

    Google Scholar 

  • Verhulst P-F (1845) “Recherches mathématiques sur la loi d’accroissement de la population.” Nouv. mém. de l’Academie Royale des Sci. et Belles-Lettres de Bruxelles 18:1–41

    Google Scholar 

  • Verhulst P-F (1847) “Deuxième mémoire sur la loi d’accroissement de la population.” Mém. de l’Academie Royale des Sci., des Lettres et des Beaux-Arts de Belgique 20:1–32

    Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Jim Duggan .

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Duggan, J. (2016). Modeling Limits to Growth. In: System Dynamics Modeling with R. Lecture Notes in Social Networks. Springer, Cham.

Download citation

  • DOI:

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-34041-8

  • Online ISBN: 978-3-319-34043-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics