J. Leonel Rocha

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In this paper is presented a relationship between the synchronization and the topological entropy. We obtain the values for the coupling parameter, in terms of the topological entropy, to achieve synchronization of two unidirectional and bidirectional coupled piecewise linear maps. In addition, we prove a result that relates the synchronizability of two(More)
In this work we develop and investigate generalized populational growth models, adjusted from Beta(p, 2) densities, with Allee effect. The use of a positive parameter C leads the presented generalization, which yields some more flexible models with variable extinction rates. An Allee limit is incorporated so that the models under study have strong Allee(More)
We present new populational growth models, generalized logistic models which are proportional to beta densities with shape parameters p and 2, where p ≫ 1, with Malthusian parameter r. The complex dynamical behaviour of these models is investigated in the parameter space (r, p), in terms of topological entropy, using explicit methods, when the(More)
The iterative elimination of the middle spacing in the random division of intervals with two points “at random” — in the narrow sense of uniformly distributed — generates a random middle Cantor set. We compute the Hausdorff dimension (which intuitively evaluates how “dense” a set is) of the random middle third(More)
Using symbolic dynamic techniques, populational growth models proportional to beta densities, are investigated. Our results give explicit methods to investigate the chaotic behaviour of populational growth models, when the malthusean parameter increases. The chaotic complexity is measured in terms of the topological entropy.
The purpose of this paper is to present a weighted kneading theory for one-dimensional maps with a hole. We consider extensions of the kneading theory of Milnor and Thurston to expanding discontinuous maps with a hole and introduce weights in the formal power series. This method allows us to derive techniques to compute explicitly the topological entropy,(More)
A dynamical approach to study the behaviour of generalized populational growth models from Beta(p, 2) densities, with strong Allee effect, is presented. The dynamical analysis of the respective unimodal maps is performed using symbolic dynamics techniques. The complexity of the correspondent discrete dynamical systems is measured in terms of topological(More)
Starting from the random extension of the Cantor middle set in [0,1], by iteratively removing the central uniform spacing from the intervals remaining in the previous step, we define random Beta(p,1)-Cantor sets, and compute their Hausdorff dimension. Next we define a deterministic counterpart, by iteratively removing the expected value of the spacing(More)