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In this paper we derive Hopf instability conditions for the morphochemical mathematical model for alloy electrodeposition introduced and experimentally validated in Bozzini et al. (J. Solid State Electrochem., 17:467-479, ). Using normal form theory we show that in the neighborhood of the Hopf bifurcation, essential features of the system dynamics are captured by a specific Complex Ginzburg-Landau Equation (CGLE). The derived CGLE yields analytical results on the existence and stability of spiral waves. Moreover, the arising of spiral instability is discussed in terms of the relevant system parameters and the related phenomenology is investigated numerically. To face with the numerical approximation of the spiral structures and of their longtime oscillating behavior we apply an Alternating Direction Implicit (ADI) method based on high order finite differences in space. [ABSTRACT FROM AUTHOR]

Alcohol dependence is among the main healthy risky behavior due to the high relevance of negative health and social effect. We study a mathematical model, given by nonlinear ordinary differential equations, describing the spread of high-risk alcohol consumption behavior within a community of individuals. We describe the peer-influence effects on alcohol addiction by assuming that susceptibles become heavy drinkers through the mechanism of imitation. We show that the model may exhibit the phenomenon of backward bifurcation. This means that alcohol problems may persist in the population even if the basic reproduction number is less than one. Nonlinear stability analysis of equilibria is also provided. [ABSTRACT FROM AUTHOR]

We consider a simple mesoscopic model of DNA in which the binding of the RNA polymerase enzyme molecule to the promoter sequence of the DNA is included through a substrate energy term modeling the enzymatic interaction with the DNA strands. We focus on the differential system for solitary waves and derive conditions-in terms of the model parameters-for the occurrence of the parametric resonance phenomenon. We find that what truly matters for parametric resonance is not the ratio between the strength of the stacking and the inter-strand forces but the ratio between the substrate and the inter-strands. On the basis of these results, the standard objection that longitudinal motion is negligible because of the second order seems to fail, suggesting that all the studies involving the longitudinal degree of freedom in DNA should be reconsidered when the interaction of the RNA polymerase with the DNA macromolecule is not neglected. [ABSTRACT FROM AUTHOR]

This paper proposes a novel mathematical model for the formation of spatio-temporal patterns in electrodeposition. At variance with classical modelling approaches that are based on systems of reaction-diffusion equations just for chemical species, this model accounts for the coupling between surface morphology and surface composition as a means of understanding the formation of morphological patterns found in electroplating. The innovative version of the model described in this work contains an original, flexible and physically straightforward electrochemical source term, able to account for charge transfer and mass transport: adsorbate-induced effects on kinetic parameters are naturally incorporated in the adopted formalism. The relevant non-linear dynamics is investigated from both the analytical and numerical points of view. Mathematical modelling work is accompanied by an extensive, critical review of the literature on spatio-temporal pattern formation in alloy electrodeposition: published morphologies have been used as a benchmark for the validation of our model. Moreover, original experimental data are presented-and simulated with our model-on the formation of broken spiral patterns in Ni-P-W-Bi electrodeposition. [ABSTRACT FROM AUTHOR]

An SEIR epidemic model with a nonlinear incidence rate is studied. The incidence is assumed to be a convex function with respect to the infective class of a host population. A bifurcation analysis is performed and conditions ensuring that the system exhibits backward bifurcation are provided. The global dynamics is also studied, through a geometric approach to stability. Numerical simulations are presented to illustrate the results obtained analytically. This research is discussed in the framework of the recent literature on the subject. [ABSTRACT FROM AUTHOR]