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Memristors (abbreviation of memory and resistor), introduced as the fourth fundamental electrical circuit element, remember the electric charge that flowed through it. These nonlinear elements are considered as a class of two terminal resistive devices and offers a lot of possible applications in various areas. In this article, we review the dynamical behaviour of some electrical circuits with memristors. Initially, we show that a simple circuit with a capacitor and an inductor connected to a memristor exhibits periodic and chaotic attractors. After that, we show that the known Chua circuit, with a nonlinear resistance, can generate bifurcations and chaos. Substituting the nonlinear resistance by a memristor, the modified Chua circuit exhibits coexistence of attractors. Another known circuit, the Colpitts, is made of a combination of capacitors and inductors containing a bipolar junction transistor. We show that the modified Colpitts circuit, created by substituting the transistor by a memristor, presents multistability and coexistence of many attractors.

Infectious diseases are caused by pathogenic microorganisms and can spread through different ways. Mathematical models and computational simulation have been used extensively to investigate the transmission and spread of infectious diseases. In other words, mathematical model simulation can be used to analyse the dynamics of infectious diseases, aiming to understand the effects and how to control the spread. In general, these models are based on compartments, where each compartment contains individuals with the same characteristics, such as susceptible, exposed, infected, and recovered. In this paper, we cast further light on some classical epidemic models, reporting possible outcomes from numerical simulation. Furthermore, we provide routines in a repository for simulations.

O presente trabalho analisa o modelo Hamiltoniano de ondas de deriva que descreve o transporte caótico de partículas no confinamento do plasma. Com apenas uma onda de deriva o sistema é integrável e apresenta órbitas regulares. Ao adicionarmos uma segunda onda, o sistema pode ou não ser integrável dependendo da velocidade de fase de cada onda. Com a mesma velocidade de fase o sistema ainda é integrável. Quando as velocidades de fase entre as duas ondas são diferentes, o sistema apresenta comportamento caótico. A este modelo acrescentamos uma pequena dissipação. Na presença de uma fraca dissipação, para certas condições iniciais, observamos órbitas transientes que convergem para atratores periódicos.