Existence of Supercritical Hopf Bifurcation on a Type-Lorenz System

In this paper, a system of Lorenz-type ordinary differential equations is considered and, under some assumptions about the parameter space, the presence of the supercritical non-degenerate Hopf bifurcation is demonstrated. The technical tool used consists of the Central Manifold theorem, a well-known formula to calculate the Lyapunov coefficient and Hopf’s Theorem. For particular values of the parameters in the parameter space established in the main result of this work, a graph is presented that describes the evolution of the trajectories, obtained by means of numerical simulation.

Hopf Bifurcation Control in a Lorenz Type System

In this paper Hopf bifurcation control is implemented in order to change the bifurcation from supercritical to subcritical in a differential equations system of Lorenz type. To achieve this purpose: first, a region of parameters is identified where the system has a supercritical Hopf bifurcation;second, a class of non-linear feedback control laws is proposed;finally, it is shown that there are control laws which the disturbed system undergoes subcritical Hopf bifurcation.

Empathy Levels of Dental Students of Central America and the Caribbean

Objective: The aim of this study is to check whether there are differences in the distribution of empathy levels in dental students from nine faculties of dentistry Colombia, Panama, Costa Rica and Dominican Republic. Methods: The levels of empathy and matrices of empathy construct matrices are estimated dental students by using the Jefferson Scale of Physician Empathy, the Spanish version for students (S version) culturally validated in Colombia, Panama, Costa Rica and Dominican Republic measured by arbitrator criteria. Cronbach α is estimated. Data of empathic orientation of the studied factors between faculties are analyzed and compared by ANOVA and Duncan test and matrices of empathy construct using discriminant analysis. Results: We find that there are differences in levels of empathy between universities, courses, gender and interaction between the Dental Faculty (University) and Course. The comparison between matrices shows unexplained variances and differences observed between the levels of empathy in student populations. Conclusions: Variability in empathy is observed in the studied factors and among student populations. The variability is an empirical finding, but is not possible in this work, to explain why.

Molecular biomarkers for oxidative stress and neuronal damage in red-bellied pacu(Piaractus brachypomus)

Biomarkers are biological molecules that provide information about the physiological condition of an organism such as early signals of health deterioration.The aim of this study was to compare the relative gene expression of four molecular biomarkers related to oxidative stress,and neuronal damage in Piaractus brachypomus under three different conditions(exposure to chlorpyrifos(CPF),menthol and eugenol anesthesia,and brain injury).Bioinformatic analyses were conducted to design primers for the molecular biomarkers,then,the relative gene expression of COX1,GPX1,BDNF and CALB1 genes was measured by qPCR using brain tissue cDNA from the treated animals as template and 2-ΔΔCT method was performed.EF1a gene was used as reference gene.The results showed a response to chemical stress in the CPF treatment samples where GPX1,BDNF and CALB1 genes were up-regulated.Finally,in menthol/eugenol and brain injury treatments,no alterations in the relative gene expression were observed.

Bats and their vital ecosystem services:a global review

Bats play crucial ecosystem services as seed dispersers,pollinators,controllers of insects,and nutrient recyclers.However,there has not been a thorough global review evaluating these roles in bats across all biogeographical regions of the world.We reviewed the literature published during the last two decades and identified 283 relevant studies:78 dealt with the control of potential insect pests by bats,80 related to the suppression of other arthropods,60 on the dispersal of native or endemic seeds,11 dealt with the dispersal of seeds of introduced plants,29 on the pollination of native or endemic plants,1 study on pollination of introduced plants,and 24 on the use of guano as fertilizer.Our literature search showed that queries combining the terms“seed dispersal,”“insectivorous bats,”“nectarivorous bats,”“use of guano,”and“ecosystem services”returned 577 studies,but half were experimental in nature.We found that the evaluation of ecosystem services by bats has been mostly conducted in the Neotropical and Palearctic regions.To detect differences across relevant studies,and to explain trends in the study of ecosystem services provided by bats,we performed generalized linear mixed models(GLMM)fitted with a Poisson distribution to analyze potential differences among sampling methods.We identified 409 bat species that provide ecosystem services,752 insect species consumed by bats and 549 plant species either dispersed or pollinated by bats.Our review summarizes the importance of conserving bat populations and the ecological services they provide,which is especially important during the current pandemic.