Necessary conditions for the existence of quasi-polynomial invariants: the quasi-polynomial and Lotka-Volterra systems

DOI10.1016/S0375-9601(99)00653-2zbMath0928.37002OpenAlexW1617979460WikidataQ127976980 ScholiaQ127976980MaRDI QIDQ1273623

Léon Brenig, Tarcísio M. Rocha Filho, Annibal Figueiredo

Publication date: 4 January 1999

Published in: Physics Letters. A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0375-9601(99)00653-2

zbMATH Keywords

Lotka-Volterra systemsnonlinear dynamical systemssemiinvariantsquasipolynomial invariants

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Smooth dynamical systems: general theory (37C99)

Related Items (8)

Reducing nonlinear dynamical systems to canonical forms ⋮ Basins of attraction of invariant regular manifolds ⋮ Permanence and boundedness of solutions of quasi-polynomial systems ⋮ Using impulses to control the convergence toward invariant surfaces of continuous dynamical systems ⋮ [SADE a Maple package for the symmetry analysis of differential equations] ⋮ An algorithm for determining a class of invariants in quasi-polynomial systems ⋮ [QPSI. A MAPLE package for the determination of quasi-polynomial symmetries and invariants] ⋮ Boundedness of solutions and Lyapunov functions in quasi-polynomial systems

Uses Software

• AUTO

Cites Work

• Singularities and groups in bifurcation theory. Volume II
• The \(1:\sqrt 2\) Hopf/steady-state mode interaction in three-dimensional magnetoconvection
• Hopf bifurcation with the symmetry of the square
• Hopf bifurcation on a square lattice

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