Strong and weak Allee effects and chaotic dynamics in Richards' growths

In this paper we define and investigate generalized Richards' growth models with strong and weak Allee effects and no Allee effect. We prove the transition from strong Allee effect to no Allee effect, passing through the weak Allee effect, depending on the implicit conditions, which involve the several parameters considered in the models. New classes of functions describing the existence or not of Allee effect are introduced, a new dynamical approach to Richards' populational growth equation is established. These families of generalized Richards' functions are proportional to the right hand side of the generalized Richards' growth models proposed. Subclasses of strong and weak Allee functions and functions with no Allee effect are characterized. The study of their bifurcation structure is presented in detail, this analysis is done based on the configurations of bifurcation curves and symbolic dynamics techniques. Generically, the dynamics of these functions are classified in the following types: extinction, semi-stability, stability, period doubling, chaos, chaotic semistability and essential extinction. We obtain conditions on the parameter plane for the existence of a weak Allee effect region related to the appearance of cusp points. To support our results, we present fold and flip bifurcations curves and numerical simulations of several bifurcation diagrams.

Synthesis of organometallic Ruthenium(II) complexes with strong activity against several human canceer cell lines

A new family of "RuCp" (Cp=eta(5)-C5H5) derivatives with bidentate N,O and N,N'-heteroaromatic ligands revealed outstanding cytotoxic properties against several human cell lines namely, A2780, A2780CisR, HT29, MCF7, MDAMB231, and PD. IC50 values were much lower than those found for cisplatin. Crystal structure of compound 4 was determined by X-ray diffraction studies. Density functional theory (DFT) calculations performed for compound 1 showed electronic flow from the ruthenium center to the coordinated bidentate ligand, in agreement with the electrochemical studies and the existence of a metal-to-ligand charge-transfer (MLCT) band evidenced by spectroscopic data.

Generalized models from Beta(p,2) densities with strong allee effect: dynamical approach

A dynamical approach to study the behaviour of generalized populational growth models from Bets(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 entropy. Different populational dynamics regimes are obtained when the intrinsic growth rates are modified: extinction, bistability, chaotic semistability and essential extinction.