Convergence to equilibrium in competitive Lotka-Volterra and chemostat systems

DOI10.1016/j.crma.2010.11.001zbMath1213.34066OpenAlexW2026225053MaRDI QIDQ616730

Nicolas Champagnat, Pierre-Emmanuel Jabin, Gaël Raoul

Publication date: 12 January 2011

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2010.11.001

zbMATH Keywords

stable equilibriumevolutionary stable strategyHolling type II

Mathematics Subject Classification ID

Population dynamics (general) (92D25) Qualitative investigation and simulation of ordinary differential equation models (34C60) Asymptotic properties of solutions to ordinary differential equations (34D05)

Related Items (15)

Dirac concentrations in a chemostat model of adaptive evolution ⋮ An asymptotic preserving scheme for capturing concentrations in age-structured models arising in adaptive dynamics ⋮ Evolution of species trait through resource competition ⋮ Measure framework for the pure selection equation: global well posedness and numerical investigations ⋮ Exactly solvable quadratic differential equation systems through generalized inversion ⋮ Selection-mutation dynamics with spatial dependence ⋮ Stacked invasion waves in a competition-diffusion model with three species ⋮ Adaptation in a stochastic multi-resources chemostat model ⋮ Global stability with selection in integro-differential Lotka-Volterra systems modelling trait-structured populations ⋮ Direct competition results from strong competition for limited resource ⋮ The evolutionary limit for models of populations interacting competitively via several resources ⋮ A probabilistic approach to Dirac concentration in nonlocal models of adaptation with several resources ⋮ From adaptive dynamics to adaptive walks ⋮ Global stability of nonhomogeneous equilibrium solution for the diffusive Lotka-Volterra competition model ⋮ Entropy Satisfying Schemes for Computing Selection Dynamics in Competitive Interactions

Cites Work

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• The evolutionary limit for models of populations interacting competitively via several resources
• Polymorphic evolution sequence and evolutionary branching
• Global asymptotic stability in Volterra's population systems
• Qualitative behavior of \(n\)-dimensional ratio-dependent predator-prey systems
• The dynamics of adaptation: An illuminating example and a Hamilton--Jacobi approach
• Systems of differential equations which are competitive or cooperative: III. Competing species
• Hopf bifurcations in competitive three-dimensional Lotka–Volterra systems
• Evolutionary Games and Population Dynamics
• The Theory of the Chemostat

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