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Bifurcation And Invariant Manifolds Of The Logistic Competition Model, M. Guzowska, Rafael Luís, Saber Elaydi
Bifurcation And Invariant Manifolds Of The Logistic Competition Model, M. Guzowska, Rafael Luís, Saber Elaydi
Mathematics Faculty Research
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.
Towards A Theory Of Periodic Difference Equations And Its Application To Population Dynamics, Saber Elaydi, Rafael Luís, Henrique Oliveira
Towards A Theory Of Periodic Difference Equations And Its Application To Population Dynamics, Saber Elaydi, Rafael Luís, Henrique Oliveira
Mathematics Faculty Research
This survey contains the most updated results on the dynamics of periodic difference equations or discrete dynamical systems this time. Our focus will be on stability theory, bifurcation theory, and on the effect of periodic forcing on the welfare of the population (attenuance versus resonance). Moreover, the survey alludes to two more types of dynamical systems, namely, almost periodic difference equations and stochastic di®erence equations.
Non-Autonomous Periodic Systems With Allee Effects, Rafael Luís, Saber Elaydi, Henrique Oliveira
Non-Autonomous Periodic Systems With Allee Effects, Rafael Luís, Saber Elaydi, Henrique Oliveira
Mathematics Faculty Research
A new class of maps called unimodal Allee maps are introduced. Such maps arise in the study of population dynamics in which the population goes extinct if its size falls below a threshold value. A unimodal Allee map is thus a unimodal map with tree fixed points, a zero fixed point, a small positive fixed point, called threshold point, and a bigger positive fixed point, called the carrying capacity. In this paper the properties and stability of the three fixed points are studied in the setting of nonautonomous periodic dynamical systems or difference equations. Finally we investigate the bifurcation of …