Logistic growth in seasonally changing environments

Abstract

We consider a parameter dependent periodic-logistic problem with a logistic term involving a degeneracy that replicates time dependent refuges in the habitat of a population. Working under no or very minimal assumptions on the boundary regularity of the domain we show the existence of a time-periodic solution which bifurcates with respect to the parameter and show their stability. We show that under suitable assumptions that the periodic solution blows up on part of the domain and remains finite on other parts when the parameter approaches a critical value.

33 pages, 2 figures

References in corpus (6)

• The role of domination and smoothing conditions in the theory of eventually positive semigroups
• Invariance of Convex Sets for Non-autonomous Evolution Equations Governed by Forms
• Periodic-parabolic eigenvalue problems with a large parameter and degeneration
• Semilinear elliptic equations on rough domains
• Asymptotic limit of linear parabolic equations with spatio-temporal degenerated potentials
• The weighted periodic-parabolic degenerate logistic equation