Limits of heteroclinic orbits in a competitive model with genetic variation

DOI10.1216/rmjm/1181073067zbMath0751.92010OpenAlexW2064128854MaRDI QIDQ1174942

James F. Selgrade

Publication date: 25 June 1992

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1216/rmjm/1181073067

zbMATH Keywords

critical valuesheteroclinic orbitsautonomous differential equationsstable coexistencemutual exclusiongenetic variationheteroclinic bifurcationallele frequency fixation planecompetition between two populationsline of polymorphic equilibriaLotka-Volterra-type equations

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Population dynamics (general) (92D25) Genetics and epigenetics (92D10)

Related Items (2)

Dynamical behavior of a competitive model with genetic variation ⋮ Results on asymptotic behaviour for discrete, two-patch metapopulations with density-dependent selection

Cites Work

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• Persistence in models of three interacting predator-prey populations
• Bifurcation of a homoclinic orbit with a saddle-node equilibrium
• Persistent unstable equilibria and closed orbits of a singularly perturbed equation
• Examples of the effect of genetic variation on competing species
• Applications of centre manifold theory
• Geometric singular perturbation theory for ordinary differential equations
• Isolated invariant sets in compact metric spaaces
• Cohomology of isolated invariant sets under perturbation
• Asymptotic Behavior for a Competitive Model with Genetic Variation
• Relaxation oscillations including a standard chase on French ducks
• Isolated Invariant Sets and Isolating Blocks

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