We extend an investigation into the bifurcation phenomena exhibited by an oxidation reaction in an adiabatic reactor to the case of a diabatic reactor. The primary bifurcation parameter is the fuel fraction; the inflow pressure and inflow temperature are the secondary bifurcation parameters. The inclusion of heat loss in the model does not change the static steady-state bifurcation diagram; the...

This paper deals with a discrete-time predator–prey system with Allee effect. We obtain asymptotically stable conditions of the equilibrium points which are subject to the Allee effect. The stabilizing effect of Allee effect on prey and predator populations is studied, respectively. The Allee effect which occurs on both of predator and prey populations is also discussed by stability analysis, p...

Abstract Analytical determination of the bifurcation thresholds is of important interest for practical electrical machine design and analysis control. This paper presents mathematical investigation of the qualitative behavior of indirect filed oriented control induction motor based on bifurcation theory. In this context, steady-state responses analysis of the motor model is discussed and an ana...

We study a boundary value problem for Willmore surfaces of revolution, where the position and the mean curvature H = 0 are prescribed as boundary data. The latter is a natural datum when considering critical points of the Willmore functional in classes of functions where only the position at the boundary is fixed. For specific boundary positions, catenoids and a suitable part of the Clifford to...

We analyze the positive solutions to  −∆v = λv(1− v); x ∈ Ω0, ∂v ∂η + γ √ λv = 0; x ∈ ∂Ω0, where Ω0 = (0, 1) or is a bounded domain in R; n = 2, 3 with smooth boundary and |Ω0| = 1, and λ, γ are positive parameters. Such steady state equations arise in population dynamics encapsulating assumptions regarding the patch/matrix interfaces such as patch preference and movement behavior. In thi...

Some new global results are given about solutions to the boundary value problem for the Euler-Lagrange equations for the Ginzburg-Landau model of a one-dimensional superconductor. The main advance is a proof that in some parameter range there is a branch of asymmetric solutions connecting the branch of symmetric solutions to the normal state. Also, simplified proofs are presented for some local...

This article deals with a two-parameter family of piecewise smooth unimodal maps with one break point. Using superstable cycles and their symbolic representation we describe the structure of the periodicity regions of the 2D bifurcation diagram. Particular attention is paid to the bistability regions corresponding to two coexisting attractors, and to the border-collision bifurca-

One of the most useful properties of dynamical systems is the existence of invariant manifolds and their invariant foliations near an equilibrium or a periodic orbit. These manifolds and foliations serve as a convenient setting to describe the qualitative behavior of the local flows, and in many cases they are useful tools for technical estimates which facilitate the study of the local bifurcat...

For domains of first kind [7,13] we describe the qualitative behavior global bifurcation diagram unbounded branch solutions Gel'fand problem crossing origin. At least to our knowledge this is result about exact monotonicity non-minimal which not just concerned with radial [28] and/or symmetric [23]. Toward goal parametrize by $L^{\infty}(\Omega)$-norm but energy associated mean field problem. T...

*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...