Oscillatory Coexistence in the Chemostat: A Codimension Two Unfolding

DOI10.1137/0143066zbMath0525.92017OpenAlexW2089212386MaRDI QIDQ3039097

James P. Keener

Publication date: 1983

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

Full work available at URL: https://doi.org/10.1137/0143066

zbMATH Keywords

chemostatmultiparameter bifurcationnumerical investigationsoscillatory coexistencecodimension two unfoldingHopf- bifurcationnontrivial branch of stable oscillatory solutionstwo predator-one prey competition model

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Population dynamics (general) (92D25) Asymptotic expansions of solutions to ordinary differential equations (34E05)

Related Items (19)

Bistability in a one-dimensional model of a two-predators-one-prey population dynamics system ⋮ Exploitative competition in a chemostat for two complementary, and possibly inhibitory, resources ⋮ Armstrong-McGehee mechanism revisited: competitive exclusion and coexistence of nonlinear consumers ⋮ The stable coexistence of competing species on a renewable resource ⋮ Poincaré Map Construction for Some Classic Two Predators–One Prey Systems ⋮ Competing predators for a prey in a chemostat model with periodic nutrient input ⋮ Current Trends in the Bifurcation Methods of Solutions of Real World Dynamical Systems ⋮ Temporal organization in a multi-species model ⋮ Oscillations induced by the time lags in limited nutrient--consumer dynamic models ⋮ Qualitative analysis of a predator-prey system with limit cycles ⋮ Persistence and coexistence in zooplankton-phytoplankton-nutrient models with instantaneous nutrient recycling ⋮ Convergence in a resource-based competition system ⋮ Global bifurcation phenomena of travelling wave solutions for some bistable reaction-diffusion systems ⋮ Coexistence of competing predators in a chemostat ⋮ Strange Periodic Attractors in a Prey-Predator System with Infected Prey ⋮ Oscillatory coexistence in a food chain model with competing predators ⋮ Bifurcations of mode equations: Spin waves ⋮ Relaxation oscillations in a class of predator-prey systems. ⋮ Estimates of size of cycle in a predator-prey system

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