Nonlinear features in whistles produced by the short-beaked common dolphin (Delphinus delphis) off southeastern Brazil.

Animal vocalizations have nonlinear characteristics responsible for features such as subharmonics, frequency jumps, biphonation, and deterministic chaos. This study describes the whistle repertoire of a short-beaked common dolphin (Delphinus delphis) group at Brazilian coast and quantifies the nonlinear features of these whistles. Dolphins were recorded for a total of 67 min around Cabo Frio, Brazil. We identify 10 basic categories of whistle, with 75 different types, classified according to their contour shape. Most (45) of these 75 types had not been reported previously for the species. The duration of the whistles ranged from 0.04 to 3.67 s, with frequencies of 3.05-29.75 kHz. Overall, the whistle repertoire presented here has one of the widest frequency ranges and greatest level of frequency modulation recorded in any study of D. delphis. All the nonlinear features sought during the study were confirmed, with at least one feature occurring in 38.4% of the whistles. The frequency jump was the most common feature (29.75% of the whistles) and the nonlinear time series analyses confirmed the deterministic chaos in the chaotic-like segments. These results indicate that nonlinearities are a relevant characteristic of these whistles, and that are important in acoustic communication.

Complex bio rhythms.

Complex biorhythms are characteristic of ubiquitous phenomena appearing in many disciplines of human knowledge. This Special Issue collects articles devoted to different complex biorhythms phenomena such as cardiac dynamics, Covid-19 dynamics, dynamics of neural networks, cell dynamics, and a few articles devoted to general methods. It furnishes a rich overview of the field and can stimulate and inspire further researches.

A dynamical map to describe COVID-19 epidemics.

Nonlinear dynamics perspective is an interesting approach to describe COVID-19 epidemics, providing information to support strategic decisions. This paper proposes a dynamical map to describe COVID-19 epidemics based on the classical susceptible-exposed-infected-recovered (SEIR) differential model, incorporating vaccinated population. On this basis, the novel map represents COVID-19 discrete-time dynamics by adopting three populations: infected, cumulative infected and vaccinated. The map promotes a dynamical description based on algebraic equations with a reduced number of variables and, due to its simplicity, it is easier to perform parameter adjustments. In addition, the map description allows analytical calculations of useful information to evaluate the epidemic scenario, being important to support strategic decisions. In this regard, it should be pointed out the estimation of the number deaths, infection rate and the herd immunization point. Numerical simulations show the model capability to describe COVID-19 dynamics, capturing the main features of the epidemic evolution. Reported data from Germany, Italy and Brazil are of concern showing the map ability to describe different scenario patterns that include multi-wave pattern with bell shape and plateaus characteristics. The effect of vaccination is analyzed considering different campaign strategies, showing its importance to control the epidemics.

COVID-19 dynamics considering the influence of hospital infrastructure: an investigation into Brazilian scenarios.

COVID-19 dynamics is one of the most relevant subjects nowadays, and, in this regard, mathematical modeling and numerical simulations are of special interest. This paper describes COVID-19 dynamics based on a novel version of the susceptible-exposed-infectious-removed model. Removed population is split into recovered and death populations allowing a better comprehension of real situations. Besides, the total population is reduced based on the number of deaths. Hospital infrastructure is also included into the mathematical description allowing the consideration of collapse scenarios. Initially, a model verification is carried out calibrating system parameters with data from China outbreak that is considered a benchmark due the availability of data for the entire cycle. Afterward, Brazil outbreak is of concern, calibrating the model and developing numerical simulations. Results show several scenarios highlighting the importance of social isolation and hospital infrastructure. System dynamics has a strong sensitivity to transmission rate showing the importance of numerical simulations to guide public health decision strategies. Results also show that complex dynamical responses can emerge due to the oscillations of the transmission rate, being associated with distinct infection subsequent waves.

A Mathematical Description of the Dynamics of Coronavirus Disease 2019 (COVID-19): A Case Study of Brazil.

This paper deals with the mathematical modeling and numerical simulations related to the coronavirus dynamics. A description is developed based on the framework of the susceptible-exposed-infectious-removed model. Initially, a model verification is carried out calibrating system parameters with data from China, Italy, Iran, and Brazil. Results show the model capability to predict infectious evolution. Afterward, numerical simulations are performed in order to analyze different scenarios of COVID-19 in Brazil. Results show the importance of the governmental and individual actions to control the number and the period of the critical situations related to the pandemic.

Random effects inducing heart pathological dynamics: An approach based on mathematical models.

This work deals with an investigation of randomness effects on heart rhythm analysis. A mathematical model composed by three-coupled nonlinear oscillators coupled by time-delayed connections is employed for this aim. In this regard, heart rhythm is governed by delayed-differential equations. Nondeterministic aspects are incorporated considering random connections among oscillators. The main idea is to show that nonlinearities and randomness define together the great variety of possibilities in the heart dynamical system. In general, results corroborate that the model is able to capture the main behaviors of the cardiac system showing that pathological behaviors can evolve from normal rhythms due to random couplings. Experimental data corroborate this argues pointing that nonlinear dynamical analysis is useful for a proper physiological comprehension.

Global warming description using Daisyworld model with greenhouse gases.

Daisyworld is an archetypal model of the earth that is able to describe the global regulation that can emerge from the interaction between life and environment. This article proposes a model based on the original Daisyworld considering greenhouse gases emission and absorption, allowing the description of the global warming phenomenon. Global and local analyses are discussed evaluating the influence of greenhouse gases in the planet dynamics. Numerical simulations are carried out showing the general qualitative behavior of the Daisyworld for different scenarios that includes solar luminosity variations and greenhouse gases effect. Nonlinear dynamics perspective is of concern discussing a way that helps the comprehension of the global warming phenomenon.