An attempt has been made to study laminar convective heat and mass transfer flow of an incompressible, viscous and electrically conducting fluid over an impulsively started vertical plate with conduction-radiation embedded in a porous medium in presence of transverse magnetic field. The influence of both second order chemical reaction and heat generation are taken into account. The governing coupled partial differential equations are solved by Crank-Nicolson method. The effects of important physical parameters on the velocity, temperature and concentration have been analyzed through graphs. The results of the present study agree well with the previous solutions. Applications of the present study are shown in material processing systems and different industries. The important findings of present study are: chemical reaction parameter acts as resistive force to reduce the velocity whereas heat source parameter enhances the velocity.

Based on the focus quantities and other techniques, the stability properties of equilibria and the limit cycles arising from Hopf bifurcations are investigated for two models of permanent magnet synchronous motors. The first model is of surface-magnet type and can have at most two unstable small limit cycles, which are symmetric with respect to $x$-axis. The other model is of interior-magnet type and can have at most four small limit cycles in two symmetric nests.

In this paper, we employ the theory of the planar dynamical system to investigate the dynamical behavior and bifurcations of solutions of the traveling systems of the $D(m,n)$ equation. On the basis of the previous work of the reference [17], we obtain the solitary cusp waves solutions (peakons and valleyons), breaking wave solutions (compactons) and other periodic cusp wave solutions. Morever, we make a summary of exact traveling wave solutions to the $D(m,n)$ system including all the solutions which have been found from the references [4, 14, 17].

Consider that infection with $Wolbachiacan$ limit a mosquito's ability to transmit Dengue fever virus through its saliva, a mathematical model describing the transmission of Dengue fever between vector mosquitoes and human, incorporating $Wolbachia$-carrying mosquito population and seasonal fluctuation, is proposed. Firstly, the stability and bifurcation of this model are investigated exactly in the case where seasonality can be neglected. Further, the basic reproductive number $\mathcal{R}_0^s$ for this model with seasonal variation is obtained, that is, if $\mathcal{R}_0^s$ is less than unity the disease is extinct and $\mathcal{R}_0^s$ is greater than unity the disease is uniformly persistent. Finally, numerical simulations verify the theoretical results. Theoretical results suggest that, compared with the mosquito reduction strategies (such as the elimination of mosquito breeding sites, killing of adult mosquitoes by spraying), introducing $Wolbachia$ strains is as effectual to fight against the transmission of Dengue virus.

The aim of this paper is twofold. Firstly, we elaborate and investigate a new trigonometric class of distribution, called the type II Tan-G class. Secondly, we perform a practical comparative evaluation of certain trigonometric classes; the Sin-G, Cos-G, Tan-G classes and the new one, with each other and with their common baseline distribution. More specifically, the usefulness and flexibility of these trigonometric classes are demonstrated through twelve practical data sets, by using the Weibull distribution as baseline. Among the data sets, two of them concern the Covid-19 pandemic in France from March to June 2020. As main results, it is shown that the related trigonometric models can outperform the former Weibull model in various cases and that the proposed type II Tan Weibull model can be, in certain situations, the best of them. The main lines of the code written in the $\textsf{R}$ software language are provided.

We investigate a class of mixed boundary value problem of nonlinear impulsive fractional differential equations with a parameter. The uniqueness of this problem is proved by applying Banach fixed point theorem.

This note extends the Bendixson-Dulac theorem to refracted systems with multiple zones. As an application, we prove that piecewise linear Duffing-type system has neither crossing limit cycles nor sliding limit cycles Therefore, it gives a positive answer to the Conjecture of [16].

In this manuscript, by using $(H,\varphi)-\eta$-monotone operators we study the existence of solution of a system of variational-like inclusion problems in Banach spaces. Further, we suggest an iterative algorithm for finding the approximate solution of this system and discuss the convergence criteria of the sequences generated by the iterative algorithm. The method used in this paper can be considered as an extension of methods for studying the existence of solution for various classes of variational inclusions considered and studied by many authors in Banach spaces.

${\it Wolbachia}$ are maternally transmitted endosymbiotic bacteria. To investigate the effect of ${\it Wolbachia}$ on the spreading and vanishing of West Nile virus, we construct a reaction-diffusion model associated with the ${\it Wolbachia}$ parameter in a heterogeneous environment, which has nonlinear infectious disease parameters. Based on the spectral radius of next infection operator and the related eigenvalue problem, we present a corresponding explicit expression describing the basic reproduction number. Furthermore, utilizing this number, we not only give out the stability of disease-free equilibrium, but also analyze the uniqueness and globally asymptotic behavior of endemic equilibrium. Our theoretical results and numerical simulations indicate that only if ${\it Wolbachia}$ reach a certain magnitude in mosquitoes, it can be effective in the control of West Nile virus.

In this paper, we are concerned with the dynamics of a diffusive predator-prey model that incorporates the functional response concerning hunting cooperation. First, we investigate the stability of the semi-trivial steady state. Then, we investigate the influence of the diffusive rates on the stability of the positive constant steady state. It is shown that there exists diffusion-driven Turing instability when the diffusive rate of the predator is smaller than the critical value, which is dependent on the diffusive rate of the prey, and the semi-trivial steady state and the positive constant steady state are both locally asymptotically stable when the diffusive rate of the predator is larger than the critical value. Finally, the nonexistence of nonconstant steady states is discussed.