Critical manifolds, travelling waves, and an example from population genetics

DOI10.1007/BF01832842zbMath0509.92014OpenAlexW1986250193WikidataQ52728360 ScholiaQ52728360MaRDI QIDQ1838915

Paul C. Fife, Charles C. Conley

Publication date: 1982

Published in: Journal of Mathematical Biology (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01832842

zbMATH Keywords

travelling wavesrandom matingcontinuous-time model of diploid populationgeneralized Morse index theoryHardy-Weinberg surfacenatural selection- migration model

Mathematics Subject Classification ID

Related Items (14)

Analysis of a continuous one-locus, two-allele genetic model with genotypic fertility differences ⋮ Charles C. Conley, 1933–1984 ⋮ Transition matrix theory ⋮ Singular limits for travelling waves for a pair of equations ⋮ Homotopy invariants of repeller-attractor pairs. I: The Puppe sequence of an R-A pair ⋮ Traveling composition waves on isothermal catalyst surfaces ⋮ Propagation of HBV with spatial dependence ⋮ Algebraic transition matrices in the Conley index theory ⋮ The conley index for fast-slow systems. II: multidimensional slow variable ⋮ Homoclinic orbits in Hamiltonian systems and heteroclinic orbits in gradient and gradient-like systems ⋮ The continuation of the Conley index for singular perturbations and the Conley indices in gradient-like systems. I ⋮ Kinetic conditions for the existence of wave fronts in reaction-diffusion systems ⋮ General conditions for the existence of a “critical point-periodic wave front” connection for reaction-diffusion systems ⋮ Small amplitude periodic waves for the FitzHugh-Nagumo equations

Cites Work

• On the persistence of spatially homogeneous solutions of a population genetics model with slow selection
• Continuous selective models
• The approach of solutions of nonlinear diffusion equations to travelling front solutions
• Multidimensional nonlinear diffusion arising in population genetics
• Dynamics of density- and frequency-dependent selection
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