Bifurcation, Chaos and Attractor in the Logistic Competition

Guzowska, Małgorzata

doi:10.2478/v10031-011-0039-5

Abstract

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.

References

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.
Search in Google Scholar
Day, R.H. (1994). Complex Economic Dynamics. The MIT Press, Cambridge, Massachusetts.
Search in Google Scholar
Elaydi, S. (1996). An Introduction to Difference Equations. Springer, New York.10.1007/978-1-4757-9168-6
Search in Google Scholar
Elaydi, S. (2008). Discrete Chaos: With Applications in Science and Engineering. Chapman and Hall/CRC.
Search in Google Scholar
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 12.10.1080/10236198.2010.504377
Search in Google Scholar
Kuznetsov, Y. (1995). Elements of applied bifurcation theory. Vol. 112 of Applied mathematical sciences, SV, New York.10.1007/978-1-4757-2421-9
Search in Google Scholar
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, 85-101.10.1016/j.chaos.2004.07.018
Search in Google Scholar
Malthus, T.R. (1798). An Essay on the Principle of Population. Printed for J. Johnson, in St. Paul's Church-Yard. London.
Search in Google Scholar
May, R.M. (1976). Simple mathematical models with very complicated dynamics. Nature 261, 459-467.10.1038/261459a0
Search in Google Scholar
Mira, C. (1987). Chaotic Dynamics. World Scientific, Singapour.10.1142/0413
Search in Google Scholar
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. 20.10.1142/2252
Search in Google Scholar
Puu, T. (1989). Nonlinear economic dynamics. In: Lecture notes in economics and mathematical systems, Vol. 336. Springer-Verlag.10.1007/978-3-662-00754-9
Search in Google Scholar
Puu, T. (1991). Chaos in business cycles. Chaos, Solitons, & Fractals. 1,457-73.10.1016/0960-0779(91)90017-4
Search in Google Scholar
Puu, T. (2000). Attractors, bifurcations, and chaos - nonlinear phenomena in economics. Springer-Verlag.
Search in Google Scholar
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.
Search in Google Scholar
Volterra, V. (1928). Variations and fluctuations of the number of individuals in animal species living together. J. Cons. Int. Explor. Mer. 3 3-51.10.1093/icesjms/3.1.3
Search in Google Scholar

Bifurcation, Chaos and Attractor in the Logistic Competition

Abstract

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