Dynamics of small autocatalytic reaction networks. I: Bifurcations, permanence and exclusion

zbMath0707.92009MaRDI QIDQ920041

Peter Schuster, Peter F. Stadler

Publication date: 1990

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

zbMATH Keywords

phase portraitsimmunologyreplicator equationidiotypic networksautocatalytic reaction networksangular parameterscatalysed multiplication of autocatalysiscatalytic RNAconstant population sizecritical surfacesdifferential equations of game dynamicsgame dynamics of Maynard- Smith models of altruismgeneric bifurcationslow-dimensional casesnon-degenerate networksnon-generic bifurcationsnon-generic transitions

Mathematics Subject Classification ID

Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.) (92C45) Biophysics (92C05) Chemical kinetics in thermodynamics and heat transfer (80A30) General biology and biomathematics (92B05)

Related Items (14)

Immune networks modeled by replicator equations ⋮ Lotka-Volterra equation and replicator dynamics: New issues in classification ⋮ Full characterization of a strange attractor. Chaotic dynamics in low- dimensional replicator systems ⋮ Permanence of sparse catalytic networks ⋮ On the coexistence of competing languages ⋮ Complementary replication ⋮ Mutation in autocatalytic reaction networks. An analysis based on perturbation theory ⋮ A model of an autocatalytic network formed by error-prone self- replicative species ⋮ Evolutionary games with affine fitness functions: applications to cancer ⋮ Estimating the probability of coexistence in cross-feeding communities ⋮ The probability of permanence ⋮ Complex dynamics of a catalytic network having faulty replication into error-species ⋮ Graph-theoretic description of the interplay between non-linearity and connectivity in biological systems ⋮ Autocatalytic networks with translation

This page was built for publication: Dynamics of small autocatalytic reaction networks. I: Bifurcations, permanence and exclusion