Untitled

Funder

Publications

A note on the bifurcation point of a randomized Fibonacci model

Publication . Luís, Rafael; Mendonça, Sandra

In a recent paper, a modified randomized Fibonacci model was presented, assuming that the number of direct offsprings of each ancestor is a Bernoulli random variable. In this work a question posted in the referred paper on the modified ran domized Fibonacci model is answered and, in addition, the model is studied from a discrete dynamical system approach. In particular, the local qualitative properties of the unique bifurcation point that emerges in the unit interval in the Randomized Fi bonacci model are presented. The work ends with a study of the long-term behaviour of a multi species ruled by the modified randomized Fibonacci model.

2016Journal article

Open access

A stochastic study for a generalized logistic model

Publication . Luís, Rafael; Mendonça, Sandra

In this paper some properties of a generalized logistic discrete model are studied. Both autonomous and non-autonomous models are addressed, as well as the stochastic model, by varying the sequence of parameters that determine the sequence of mappings of the process. Some results on stability are established and the long-term behaviour of the orbits is studied.

2021Journal article

Open access

Local stability in 3D discrete dynamical systems: application to a Ricker competition model

Publication . Luís, Rafael; Rodrigues, Elias

A survey on the conditions of local stability of fixed points of three-dimensional discrete dynamical systems or difference equations is provided. In particular, the techniques for studying the stability of nonhyperbolic fixed points via the centre manifold theorem are presented. A nonlinear model in population dynamics is studied, namely, the Ricker competition model of three species. In addition, a conjecture about the global stability of the nontrivial fixed points of the Ricker competition model is presented.

2017Journal article

Open access