On the Cyclic Replicator Equation and the Dynamics of Semelparous Populations

DOI10.1137/080722734zbMath1179.34044OpenAlexW2091060447MaRDI QIDQ3182054

Odo Diekmann, Stephan A. van Gils

Publication date: 2 October 2009

Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/080722734

zbMATH Keywords

Lotka-Volterrareplicator equationsemelparity

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcation theory for ordinary differential equations (34C23) Population dynamics (general) (92D25) Qualitative investigation and simulation of ordinary differential equation models (34C60) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

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Control problems with vanishing Lie bracket arising from complete odd circulant evolutionary games ⋮ Invasibility of nectarless flowers in plant-pollinator systems ⋮ Exclusion of dominated species in open replicator systems ⋮ Evolutionary dynamics of a multi-trait semelparous model ⋮ Periodic orbits near heteroclinic cycles in a cyclic replicator system ⋮ Permanence induced by life-cycle resonances: the periodical cicada problem ⋮ A nonlinear continuous-time model for a semelparous species ⋮ Synchrony and the Dynamic Dichotomy in a Class of Matrix Population Models ⋮ Boundary dynamics of the replicator equations for neutral models of cyclic dominance ⋮ Asymptotic Poincaré maps along the edges of polytopes ⋮ Bifurcations of cycles in nonlinear semelparous Leslie matrix models ⋮ Fixation time of the rock-paper-scissors model: rigorous results in the well-mixed setting ⋮ Circulant games

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