Bifurcation, Chaos and Attractor in the Logistic Competition

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.10.1007/978-1-4757-9168-6Search 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 12.10.1080/10236198.2010.504377Search in Google Scholar

Kuznetsov, Y. (1995). Elements of applied bifurcation theory. Vol. 112 of Applied mathematical sciences, SV, New York.10.1007/978-1-4757-2421-9Search 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.2004.07.018Search 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, 459-467.10.1038/261459a0Search in Google Scholar

Mira, C. (1987). Chaotic Dynamics. World Scientific, Singapour.10.1142/0413Search 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. 20.10.1142/2252Search in Google Scholar

Puu, T. (1989). Nonlinear economic dynamics. In: Lecture notes in economics and mathematical systems, Vol. 336. Springer-Verlag.10.1007/978-3-662-00754-9Search in Google Scholar

Puu, T. (1991). Chaos in business cycles. Chaos, Solitons, & Fractals. 1,457-73.10.1016/0960-0779(91)90017-4Search 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/3.1.3Search in Google Scholar