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.
Taylor & Francis
Guzowska, M., Luís, R., & Elyadi, S. (2011). Bifurcation and invariant manifolds of the logistic competition model. Journal of Difference Equations and Applications, 17(12), 1851-1872. doi: 10.1080/10236198.2010.504377
Journal of Difference Equations and Applications