A permanence theorem for replicator and Lotka-Volterra systems

DOI10.1007/BF00277165zbMath0647.92021WikidataQ113909011 ScholiaQ113909011MaRDI QIDQ1104891

Wolfgang Jansen

Publication date: 1987

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

zbMATH Keywords

Lotka-Volterra equationsboundarypower functionrepellerreplicator equationscompact invariant setcompact state spacedual programming problemexistence of an average Lyapunov functionpolyhedral state spacessufficient criterion for permanence

Mathematics Subject Classification ID

Linear programming (90C05) Population dynamics (general) (92D25) Ecology (92D40) Stability theory for ordinary differential equations (34D99) Dynamical systems and ergodic theory (37-XX)

Related Items (35)

Permanence in Lotka-Volterra equations: Linked prey-predator systems ⋮ Stochastic population dynamics under regime switching ⋮ Coexistence for systems governed by difference equations of Lotka- Volterra type ⋮ Almost necessary and sufficient conditions for survival of species ⋮ Permanence of sparse catalytic networks ⋮ A unified approach to persistence ⋮ Permanence for three species with cyclic loop ⋮ Repellers in systems with infinite delay ⋮ Cross-feeding dynamics described by a series expansion of the replicator equation ⋮ Parasite species richness and its effect on persistence in food webs ⋮ Conservative and dissipative polymatrix replicators ⋮ Keystone species and vulnerable species in ecological communities: strong or weak interactors? ⋮ Dissipation, boundedness and persistence of general ecological systems ⋮ Uniform persistence and global stability of two prey-predator pairs linked by competition ⋮ Effects of dynamics on ecological networks ⋮ On the generality of stability-complexity relationships in Lotka-Volterra ecosystems ⋮ Permanence induced by life-cycle resonances: the periodical cicada problem ⋮ Permanence in polymatrix replicators ⋮ Permanence of stochastic Lotka-Volterra systems ⋮ Global stability of interior and boundary fixed points for Lotka-Volterra systems ⋮ Permanence and the dynamics of biological systems ⋮ Environmental Brownian noise suppresses explosions in population dynamics. ⋮ Dynamics of an ecological system ⋮ On permanence of all subsystems of competitive Lotka-Volterra systems with delays ⋮ Is there switching for replicator dynamics and bimatrix games? ⋮ Average growth and total permanence in a competitive Lotka-Volterra System ⋮ Asymptotic Poincaré maps along the edges of polytopes ⋮ The probability of permanence ⋮ Two predators feeding on two prey species: A result on permanence ⋮ Permanence of some ecological systems with several predator and one prey species ⋮ On the stabilizing effect of predators and competitors on ecological communities ⋮ Stochastic population dynamics under regime switching. II ⋮ Criteria for \(C^r\) robust permanence ⋮ Shaken not stirred: On permanence in ecological communities ⋮ MOLECULAR REPLICATOR DYNAMICS

Cites Work

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• A general cooperation theorem for hypercycles
• Selfregulation of behaviour in animal societies. I. Symmetric contests
• Dynamical systems under constant organization. I: Topological analysis of a family of non-linear differential equations - a model for catalytic hypercycles

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