In this work, we study an epidemic model with vaccination and vertical transmission. We get the basic reproduction number R0 of the system and carry out a bifurcation analysis and obtain the conditions ensuring that the system exhibits backward bifurcation. Mathematics Subject Classification : 34C05, 92D25

*Correspondence: [email protected] Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, China Abstract The main objective of this paper is to investigate the dynamic bifurcation for the granulation convection in the solar photosphere. Based on the dynamic bifurcation theory, which is established by Ma and Wang (Phase transition dynamics, pp. 380-459, 2014), the critical pa...

We report on some recent existence and uniqueness results for elliptic equations subject to Dirichlet boundary condition and involving a singular nonlinearity. We take into account the following types of problems: (i) singular problems with sublinear nonlinearity and two parameters; (ii) combined effects of asymptotically linear and singular nonlinearities in bifurcation problems; (iii) bifurca...

In this paper, we establish a Hopf bifurcation theorem for abstract Cauchy problems in which the linear operator is not densely defined and is not a Hille–Yosida operator. The theorem is proved using the center manifold theory for nondensely defined Cauchy problems associated with the integrated semigroup theory. As applications, the main theorem is used to obtain a known Hopf bifurcation resul...

A Hopf-bifurcation scenario with symmetries is studied. Here, apart from the well known branches of periodic solutions, other bifurcation phenomena have to occur as it is shown in the second part of the paper using topological arguments. In this rst part of the paper we prove analytically that invariant tori with quasiperiodic motion bifurcate. The main methods used are orbit space reduction an...

This paper presents the stability and bifurcation analysis of a dynamical model of the heartbeat with time delay. The existence of Hopf bifurcations at the positive equilibrium is established by analyzing the distribution of the characteristic values. Moreover, the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are determinated by applying the center m...

In this paper, we consider a three-component reaction-diffusion system with a chemorepulsion. The purpose of this work is to analyze the chemotactic effects due to the gradient of the chemotactic sensitivity and the shape of the interface. Conditions for existence of stationary solutions and Hopf bifurcation in the interfacial problem as the bifurcation parameters vary are obtained analytically...

In this paper, a kind of nonlinear delayed differential equations which can describe an economic model is considered. In this economy, population is modelled according to a logistically variable carrying capacity and capital’s accumulation has a time delay. By choosing time delay as a bifurcation parameter, it is proved that the system loses stability and a Hopf bifurcation occurs when the time...