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.

Como aplicação didática da Relatividade Geral, implementamos, a partir da métrica de Schwarzschild, uma simulação da órbita da estrela S2 em torno do buraco negro massivo Sagitário A*. Verificamos que a orbita simulada é quase uma elipse, com uma precessão lenta igual à observada recentemente. Nessa simulação utilizamos os aplicativos Geogebra e Excel. Geral implementamos Schwarzschild S A A* elipse recentemente Excel

As a didactic application of General Relativity and based on the Schwarzschild metric, a simulation of the orbit of the star S2 around the massive black hole Sagittarius A* is implemented. We verified that the simulated orbit is almost an ellipse, with a slow precession equal to the one recently observed. This simulation is performed using Geogebra and Excel applications. metric S A implemented ellipse observed applications

Mapas simpléticos podem fornecer o mais simples e preciso modo de visualizar e quantificar a dinâmica de sistemas conservativos de dois graus de liberdade. Esses mapas podem ser facilmente iterados com os mais simples dos computadores, obtendo trajetórias com grande precisão. Esses mapas aparecem em muitas áreas, incluindo mecânica celestial, física de plasmas, química etc. Nesse artigo serão introduzidos dois exemplos de mapas simpléticas, o mapa padrão e o mapa padrão não-twist, explorando a transformação do espaço de fase conforme os parâmetros de controle são alterados. Além disso, também apresentamos, para mapas não-twist, que o movimento caótico é separado no espaço de fase pela barreira de transporte não-twist. liberdade computadores precisão áreas celestial plasmas etc simpléticas nãotwist, nãotwist não twist, twist não-twist alterados disso apresentamos nãotwist. twist.

Symplectic maps can provide a straightforward and accurate way to visualize and quantify the dynamics of conservative systems with two degrees of freedom. These maps can be easily iterated from the simplest computers to obtain trajectories with great accuracy. Their usage arises in many fields, including celeste mechanics, plasma physics, chemistry, and so on. In this paper we introduce two examples of symplectic maps, the standard map and the standard non-twist map, exploring the phase space transformation as their control parameters are varied. Furthermore, for the non-twist map, we also present, that its chaotic motion is separated in phase space by the non-twist transport barrier. freedom accuracy fields mechanics physics chemistry on nontwist non twist varied Furthermore present barrier

Osciladores de fase são sistemas dinâmicos dissipativos com aporte externo de energia, e matematicamente caracterizados pela presença de ciclos-limite, ao longo dos quais a dinâmica pode ser descrita por um ângulo de fase. No presente artigo, consideramos fenômenos de sincronização num sistema de muitos osciladores de fase acoplados. Adotamos uma descrição qualitativa, baseada num modelo paradigmático proposto por Y. Kuramoto em 1975. Discutimos, à luz dessa descrição, algumas aplicações em sistemas físicos (metrônomos e pedestres numa ponte pênsil) e biológicos (neurônios e vagalumes piscando).

Phase oscillators are dissipative dynamic systems with external energy input, and mathematically characterized by the presence of limit cycles, along which the dynamics can be described by a phase angle. In the present article, we consider synchronization phenomena in a system of many phase-coupled oscillators. We adopt a qualitative description, based on a paradigmatic model proposed by Y. Kuramoto in 1975. We discuss, in the light of this description, some applications in physical systems (metronomes and pedestrians on a suspension bridge) and biological (neurons and fireflies blinking).

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.

<p>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.</p>

<p>This paper analyses the Hamiltonian model of drift waves which describes the chaotic transport of particles in the plasma confinement. With one drift wave the system is integrable and it presents stable orbits. When one wave is added the system may or may not be integrable depending on the phase of each wave velocity. If the two waves have the same phase velocity, the system is integrable. When the phase velocities between the two waves are different, the system shows chaotic behaviour. In this model we add a small dissipation. In the presence of a weak dissipation, for different initial conditions, we observe transient orbits which converge to periodic attractors.</p>

<p>Neste artigo, investigamos a sincronização de disparos neuronais em uma rede neuronal com plasticidade sináptica e perturbação externa. Nas simulações, a dinâmica neuronal é descrita pelo modelo de Hodgkin-Huxley, considerando sinapses químicas (excitatórias) entre neurônios. De acordo com a sincronização dos disparos é esperado que uma perturbação cause regimes não sincronizados. No entanto, na literatura existem trabalhos que mostram que a combinação de plasticidade sináptica e perturbação externa podem gerar regime sincronizado. Este artigo descreve o efeito da plasticidade sináptica na sincronização, onde consideramos a perturbação descrita por uma distribuição uniforme. Este estudo é relevante para pesquisas de controle de distúrbios neuronais.</p>

<p>In this paper, we investigated the neural spikes synchronisation in a neural network with synaptic plasticity and external perturbation. In the simulations the neural dynamics is described by the Hodgkin Huxley model considering chemical synapses (excitatory) among neurons. According to neural spikes synchronisation is expected that a perturbation produce non synchronised regimes. However, in the literature there are works showing that the combination of synaptic plasticity and external perturbation may generate synchronised regime. This article describes the effect of the synaptic plasticity on the synchronisation, where we consider a perturbation with a uniform distribution. This study is relevant to researches of neural disorders control.</p>

In this work it is considered the effect of an ergodic magnetic limiter on the plasma confined in the TCABR tokamak. The poloidal distribution of the limiter currents is determined taking into account the toroidal geometry of this tokamak. The plasma equilibrium field is analytically obtained by solving the Grad-Schlüter-Shafranov equation in polar toroidal coordinates. The perturbing limiter field is obtained as a vacuum field by solving the Laplace equation. Supposing the limiter action as a sequence of delta-function pulses, a symplectic map is derived by using a Hamiltonian formulation for the perturbed field line. Examples are given to illustrate the influence of this design on the topology of the perturbed field line structure.