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2011 | 10 | nr 2 | 7--18
Tytuł artykułu

Bifurcation, Chaos and Attractor in the Logistic Competition

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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. (original abstract)
Rocznik
Tom
10
Numer
Strony
7--18
Opis fizyczny
Twórcy
  • University of Szczecin, Poland
Bibliografia
  • 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.
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  • 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.
  • 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.
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Bibliografia
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bwmeta1.element.ekon-element-000171205295

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