We consider a singularly perturbed bistable reaction diffusion equation in a one-dimensional spatially degenerate inhomogeneous media. Degeneracy arises due to the choice of spatial inhomogeneity from some well-known class of normal forms or universal unfoldings. By means of a bilinear double well potential, we explicitly demonstrate the similarities and discrepancies between the bifurcation ph...

This paper considers a mathematical model based on the transmission dynamics of hepatitis C virus (HCV) infection. In addition to the usual compartments for susceptible, exposed, and infected individuals, this model includes compartments for individuals who are under treatment and those who have had vaccination against HCV infection. It is assumed that the immunity provided by the vaccine fades...

In this paper we investigate the properties and linear stability of travelling premixed combustion waves and the formation of pulsating combustion waves in a model with two-step chain-branching reaction mechanism. These calculations are undertaken in the adiabatic limit, in one spatial dimension and for the case of arbitrary Lewis numbers for fuel and radicals. It is shown that the Lewis number...

We present a deterministic mathematical model for malaria transmission with waning immunity. The model consists of five non-linear system of differential equations. We used next generation matrix to derive the basic reproduction number R0. The disease free equilibrium was computed and its local stability has been shown by the virtue of the Jacobean matrix. Moreover, using Lyapunov function theo...

We report experimental results for convection near onset in a thin layer of a homeotropically aligned nematic liquid crystal heated from below as a function of the temperature difference DT and the applied vertical magnetic field H . When possible, these results are compared with theoretical calculations. The experiments were done with three cylindrical cells of aspect ratios @~radius!/~height!...

Neural networks are applied to a theoretical subject in developmental psychology: modeling developmental transitions. Two issues that are involved will be discussed: discontinuities and acquiring qualitatively new knowledge. We will argue that by the appearance of a bifurcation, a neural network can show discontinuities and may acquire qualitatively new knowledge. First, it is shown that biolog...

We develop a theory of collective phase description for globally coupled noisy excitable elements exhibiting macroscopic oscillations. Collective phase equations describing macroscopic rhythms of the system are derived from Langevin-type equations of globally coupled active rotators via a nonlinear Fokker-Planck equation. The theory is an extension of the conventional phase reduction method for...

In this paper, a bifurcation analysis of a recently proposed reduced order cardiac cell model is performed to obtain insights into the mechanisms of control of the sinoatrial node pacemaker activity. The objective is to improve the understanding of cardiac arrhythmias caused by abnormal automaticity. The bifurcation structure of the model is studied as a function of the maximal conductances of ...

| A novel observer for tracking and identifying a chaotic system with time-varying bifurcation parameters via an observation signal contaminated by additive white Gaussian noise (AWGN) is developed in this paper. It is realized by an adaptive algorithm which takes advantage of the good approximation capability of the Radial Basis Function (RBF) neural network and the ability of the Extended Kal...

In this paper, we shall establish unilateral global bifurcation result for a class of fourthorder eigenvalue problems with sign-changing weight. Under some natural hypotheses on perturbation function, we show that lk;0 is a bifurcation point of the above problems and there are two distinct unbounded continua, Ck þ and Ck , consisting of the bifurcation branch Ck from lk;0 , wher e lk is the kth...