The stability of travelling wave solutions of singularly perturbed, diffusive predator-prey systems is proved by showing that the linearized operator about such a solution has no unstable spectrum and that the translation eigenvalue at k 0 is simple. The proof illustrates the application of some recently developed geometric and topological methods for counting eigenvalues.

In this paper, we consider a mathematical model motivated by patterned growth of bacteria. The model is a system of differential equations that consists of two sub-systems. One is a system of ordinary differential equations and the other one is a reaction-diffusion system. Pattern formation in this model is caused by an initial instability of the ordinary differential equations. However, nonlin...

Wu’s elimination method is an important method for solving multivariate polynomial equations. In this paper, we apply interval arithmetic to Wu’s method and convert the problem of solving polynomial equations into that of solving interval polynomial equations. Parallel results such as zero-decomposition theorem are obtained for interval polynomial equations. The advantages of the new approach a...

In this study, a realistic model for dynamic instability of embedded single-walled nanotubes (SWCNTs) conveying pulsating fluid is presented considering the viscoelastic property of the nanotubes using Kelvin–Voigt model. SWCNTs are placed in longitudinal magnetic fields and modeled by sinusoidal shear deformation beam theory (SSDBT) as well as modified couple stress theory. The effect of slip ...

In this note we give an alternative, shorter proof of the classical result of Berestycki and Cazenave on the instability by blow-up for the standing waves of some nonlinear Schrödinger equations.

We study the ecological and mathematical significance of a nonlinear discrete predator–prey model that includes several types of self-limitation on the prey. The model is derived for the dynamics of two interacting populations where predators feed only on prey of a certain age. We show how the introduction of different limitation factors can account for several important phenomena that affect t...

The laminar boundary layer and the position o j the transit l vn point xcre inzedigaied on a heated $at plate. I t was fuund thaf the Reynolds nxrnber of transition decreases as the ttmperature oj the plate i s increased. I t i s shuwn from simple qualitatire analytical considerations thaf the e#mt of rariable ~Gscosity in the bvundary laycr due to the temperature di8erence produces a relocity ...

We consider a general model for predator-prey interactions in which the instantaneous per unit growth rate j i — ft(Nv N2)(t) of each species at any time t is a functional of species densities N^s) at previous times s ^ t. We assume that the equation for prey density Nx obtained from the model in the absence of predators (N2 — 0) possesses at least one positive equilibrium c > 0 (which may or m...

We prove instability of a part of a branch of viscous incompressible fluid flows induced by a shrinking sheet. These flows are exact solutions of the Navier-Stokes equation.

When an elastic filament spins in a viscous incompressible fluid it may undergo a whirling instability, as studied asymptotically by Wolgemuth, Powers, and Goldstein [Phys. Rev. Lett., 84 (2000), pp. 16–23]. We use the immersed boundary (IB) method to study the interaction between the elastic filament and the surrounding viscous fluid as governed by the incompressible Navier–Stokes equations. T...