Jump to ContentJump to Main Navigation
Show Summary Details

Folia Oeconomica Stetinensia

The Journal of University of Szczecin

Open Access
See all formats and pricing

Bifurcation, Chaos and Attractor in the Logistic Competition

Małgorzata Guzowska1

Department of Econometrics and Statistics, Faculty of Economics and Management, University of Szczecin, Mickiewicza 64, 71-101 Szczecin1

This content is open access.

Citation Information: Folia Oeconomica Stetinensia. Volume 10, Issue 2, Pages 7–18, ISSN (Online) 1898-0198, ISSN (Print) 1730-4237, DOI: https://doi.org/10.2478/v10031-011-0039-5, June 2012

Publication History

Published Online:

Bifurcation, Chaos and Attractor in the Logistic Competition

This paper deals with a two-dimensional discrete time competition model. The corresponding twodimensional iterative map is represented in terms of its bifurcation diagram in the parameter plane. A number of bifurcation sequences for attractors and their basins are studied.

Keywords: Discrete Logistic Competition Model; local stability; global stability; bifurcation; chaos; chaotic attractor

  • Bischi, G.I., Gardini, L. (2000). Global Properties of Symmetric Competition Models with Riddling and Blowout Phenomena. Discrete Dynamics in Nature and Society. Vol. 5, 149-160.

  • Day, R.H. (1994). Complex Economic Dynamics. The MIT Press, Cambridge, Massachusetts.

  • Elaydi, S. (1996). An Introduction to Difference Equations. Springer, New York.

  • Elaydi, S. (2008). Discrete Chaos: With Applications in Science and Engineering. Chapman and Hall/CRC.

  • Guzowska, M., Luis, R., Elaydi, S. (2011). Bifurcation and invariant manifolds of the logistic competition model. Journal of Difference Equations and Applications. Vol. 17, Issue 12. [Web of Science]

  • Kuznetsov, Y. (1995). Elements of applied bifurcation theory. Vol. 112 of Applied mathematical sciences, SV, New York.

  • López-Ruiz, R., Fournier-Prunaret, D. (2004). Indirect Allee effect, bistability and chaotic oscillations in a predator-prey discrete model of logistic type. Chaos, Solitons and Fractals, 24, 85-101.

  • Malthus, T.R. (1798). An Essay on the Principle of Population. Printed for J. Johnson, in St. Paul's Church-Yard. London.

  • May, R.M. (1976). Simple mathematical models with very complicated dynamics. Nature 261, 459-467.

  • Mira, C. (1987). Chaotic Dynamics. World Scientific, Singapour.

  • Mira, C., Gardini, L., Barugola, A., Cathala, J.-C. (1996). Chaotic Dynamics in Two- Dimensional Noninvertible Maps. World Scientific Series on Nonlinear Science. Series A, Vol. 20.

  • Puu, T. (1989). Nonlinear economic dynamics. In: Lecture notes in economics and mathematical systems, Vol. 336. Springer-Verlag.

  • Puu, T. (1991). Chaos in business cycles. Chaos, Solitons, & Fractals. 1,457-73.

  • Puu, T. (2000). Attractors, bifurcations, and chaos - nonlinear phenomena in economics. Springer-Verlag.

  • Verhulst, P.F. (1845). Recherches mathématiques sur la loi d'accroissement de la population. Nouveaux Mémoires de l'Académie Royale des Sciences et Belles-Lettres de Bruxelles 18,1-42.

  • Volterra, V. (1928). Variations and fluctuations of the number of individuals in animal species living together. J. Cons. Int. Explor. Mer. 3 3-51.

Comments (0)

Please log in or register to comment.