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Bifurcation and Invariant Manifolds of the Logistic Competition Model
Journal of Difference Equations and Applications
  • Malgorzata Guzowska, University of Szczecin
  • Rafael Luis, Technical University of Lisbon
  • Saber Elaydi, Trinity University
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In this paper we study a new logistic competition model. We will investigate stability and bifurcation of the model. In particular, we compute the invariant manifolds, including the important center manifolds, and study their bifurcation. Saddle-node and period doubling bifurcation route to chaos is exhibited via numerical simulations.

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Guzowska, M., LuĂ­s, R., & Elyadi, S. (2011). Bifurcation and invariant manifolds of the logistic competition model. Journal of Difference Equations and Applications, 17, 1851-1872. doi: 10.1080/10236198.2010.504377