No full-text available
To read the full-text of this research,
you can request a copy directly from the authors.
Logistic Models with Diffusions
Abstract
Population dispersal
plays an important role in the population dynamics which arises from environmental and ecological gradients in the habitat. We assume that the systems under consideration are allowed to diffuse spatially besides evolving in time. The spatial diffusion arises from the tendency of species to migrate towards regions of lower population density where the life is better. The most familiar model systems incorporating these features are reaction diffusion equations.
ResearchGate has not been able to resolve any citations for this publication.
Alternative problems : An historical perspective.- Coincidence degree for perturbations of Fredholm mappings.- A generalized continuation theorem and existence theorems for Lx = Nx.- Two-point boundary value problems : Nonlinearities without special structure.- Approximation of solutions - The projection method.- Quasibounded perturbations of Fredholm mappings.- Boundary-value problems for some semilinear elliptic partial differential equations.- Periodic solutions of ordinary differential equations with quasibounded nonlinearities and of functional differential equations.- Coincidence index, multiplicity and bifurcation theory.- Coincidence degree for k-set contractive perturbations of linear Fredholm mappings.- Nonlinear perturbations of fredholm mappings of nonzero index.
The purpose of this article is to derive a set of ‘easily verifiable’ sufficient conditions for the local asymptotic stability of the trivial solution of
and then examine the ‘size’ of the domain of attraction of the trivial solution of the nonlinear system (1·1) with a countable number of discrete delays.
In this paper, we consider the following logistic equation with piecewise constant arguments: {dN(t)/dt=rN(t){1-∑j=0majN([t-j])}, t≥0, m≥1, N(0)=N0>0, N(-j)=N-j≥0, j=1,2,...,m, where r>0, a0,a1, ...,am≥0, ∑j=0m aj>0, and [x] means the maximal integer not greater than x. The sequence {Nn}n=0∞, where Nn=N(n), n=0,1,2,... satisfies the difference equation Nn+1=Nnexp{ r(1-∑j=0m aj Nn-j n=0,1,2,.... Under the condition that the first term a0 dominates the other m coefficient s ai, 1≤i≤m, we establish new sufficient conditions of the global asymptotic stability for the positive equilibrium N*= 1/(∑j=0maj).