Integrability and singularity structure of predator-prey system

DOI10.1063/1.530023zbMath0780.34003OpenAlexW2015625088WikidataQ115553614 ScholiaQ115553614MaRDI QIDQ3141395

Sharadha Ramanan, P. L. Sachdev

Publication date: 23 January 1994

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

Full work available at URL: https://doi.org/10.1063/1.530023

zbMATH Keywords

first integralsformal seriesmovable singularityPainlevéextended ARS (Ablowitz, Ramani, and Segur) algorithmtwo-dimensional predator- prey system

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Population dynamics (general) (92D25) Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35)

Related Items (6)

Generic predation in age structure predator-prey models ⋮ Lie symmetries and invariants of the Lotka–Volterra system ⋮ Finite-time blow-up in dynamical systems ⋮ Necessary and sufficient conditions for finite time singularities in ordinary differential equations ⋮ Painlevé analysis and normal forms theory ⋮ On certain new integrable second order nonlinear differential equations and their connection with two dimensional Lotka–Volterra system

Cites Work

• Bifurcation of solutions and the nonexistence of first integrals in Hamiltonian mechanics. I
• Investigations into a class of generalized two-dimensional Lotka-Volterra schemes
• A survey of quadratic systems
• Integrability and the Painlevé property for low-dimensional systems
• A connection between nonlinear evolution equations and ordinary differential equations of P-type. I
• The Painlevé-Kowalevski and Poly-Painlevé Tests for Integrability
• Qualitative investigation of a system of differential equations of the theory of oscillations
• Necessary condition for the existence of algebraic first integrals

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