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Classification of the Dynamical Behaviour of a Piecewise Oscillator

Santos, Ana I.; Ramos, Carlos C.; Vinagre, Sandra

We consider a forced damped oscillator whose motion is modeled by a second-order non-autonomous piecewise linear differential equation. The system has a continuous regime, where the time flow is characterized by the explicit solutions of ordinary differential equations, and a singular regime, where the time flow is characterized by an appropriate transformation relating the explicit solutions from one domain to...


On lattices from combinatorial game theory: infinite case

Carvalho, Alda; Santos, Carlos; Dias, Cátia; Coelho, Francisco; Neto, João Pedro; Nowakowski, Richard; Vinagre, Sandra

Given a set of combinatorial games, the children are all those games that can be generated using as options the games of the original set. It is known that the partial order of the children of all games whose birthday is less than a fixed ordinal is a distributive lattice and also that the children of any set of games form a complete lattice. We are interested in the converse. In a previous paper, we showed tha...


Dynamics of a Certain Nonlinearly Perturbed Heat Equation

Ramos, Carlos; Santos, Ana Isabel; Vinagre, Sandra

We consider a system described by the linear heat equation, with appropriate boundary conditions in order to model the temperature on a wire with adiabatic endpoints, which is perturbed nonlinearly by a family of quadratic maps. The time instants of the perturbation are determined by an additional dynamical system, seen here as part of the external interacting system. We study the complex behaviour of the syste...


The Dynamics of a Hybrid Chaotic System

Ramos, Carlos; Santos, Ana Isabel; Vinagre, Sandra

We consider a forced damped piecewise linear oscillator whose motion is modeled by the second-order non-autonomous differential equation. Our hybrid chaotic system has a continuous regime, where the time flow is characterized by the explicit solutions of the ordinary differential equations, and a singular regime, where the time flow is characterized by an appropriate transformation linking the explicit solution...


On lattices from combinatorial game theory: infinite case

Carvalho, Alda; Santos, Carlos; Dias, Cátia; Coelho, Francisco; Neto, João P.; Nowakowski, Richard; Vinagre, Sandra

Given a set of combinatorial games, the children are all those games that can be generated using as options the games of the original set. It is known that the partial order of the children of all games whose birthday is less than a fxed ordinal is a distributive lattice and also that the children of any set of games form a complete lat tice. We are interested in the converse. In a previous paper, we showed tha...


The use of medicinal plants by the population from the Protected Landscape of “...

Vinagre, Cidália; Vinagre, Sandra; Carrilho, Ermelinda

Background: Traditional medicine has an important role in local communities, who use plants in the treatment of various diseases. The research of traditional uses of medicinal plants allows us to document and analyze ethnopharmacological practices. This paper reports on an ethnobotanical survey that was conducted in the Protected Landscape of the “Serra de Montejunto”, a Portuguese area in the west of the Iberi...


Asymptotic Behaviour in a Certain Nonlinearly Perturbed Heat Equation: Non Peri...

Ramos, Carlos; Santos, Ana Isabel; Vinagre, Sandra

We consider a system described by the linear heat equation with adiabatic boundary conditions.We impose a nonlinear perturbation determined by a family of interval maps characterized by a certain set of parameters. The time instants of the perturbation are determined by an additional dynamical system, seen here as part of the external interacting system. We analyse the complex behaviour of the system, through t...


The mathematics and the art of crochet in the world of illusions

Martins, Maria do Carmo; Melo, Helena; Vinagre, Sandra

When, around 1800, the French El eonore Riego de la Branchardi ere began to draw embroidery patterns to crochet that could be used and reproduced by enthusiastic followers of this technique, she was far from thinking that, stitch by stitch, round by round, crochet paves the plane and the plane paved is confused with 3D space. This work illustrates how to apply Mathematics to art of crochet harmoniously and how ...


Ethnobotanical study in the protected landscape “Serra de Montejunto” (Portugal)

Vinagre, Cidália; Vinagre, Sandra; Carrilho, Ermelinda; García, D.; Vázquez, Francisco; Pinto-Gomes, Carlos

Since ancient times, the human being has been using plants for their benefit, as food, condiments, drugs and flavors, accumulating knowledge that allowed him to add other applications, whose memory, in some cases, could reach present time. In order to investigate the surviving contents of this collective memory, this work reports an ethnobotanical survey that was carried out in 2014 in the Protected Landscape “...


A symbolic approach to nonlinearly perturbed heat equation

Ramos, Carlos; Santos, Ana Isabel; Vinagre, Sandra

We consider a system described by the linear heat equation with adiabatic boundary conditions which is perturbed periodicaly. This perturbation is nonlinear and is characterized by a one-parameter family of quadratic maps. The system, depending on the parameters, presents very complex behaviour. We introduce a symbolic framework to analyze the system and resume its most important features.


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