Periodic orbits of a non-autonomous quadratic differential system obtained from third-order differential equations

DOI10.1080/14689367.2011.638274zbMath1243.37045OpenAlexW2055645279MaRDI QIDQ2904329

Jaume Llibre, Amar Makhlouf

Publication date: 13 August 2012

Published in: Dynamical Systems (Search for Journal in Brave)

Full work available at URL: http://ddd.uab.cat/record/150497

zbMATH Keywords

third-order differential equationperiodic orbitquadratic systemaveraging theory

Mathematics Subject Classification ID

Averaging method for ordinary differential equations (34C29) Dynamics induced by flows and semiflows (37C10) Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Complex behavior and chaotic systems of ordinary differential equations (34C28)

Cites Work

• Quadratic vector fields in the plane have a finite number of limit cycles
• A new chaotic attractor
• An equation for continuous chaos
• POLYNOMIAL VECTOR FIELDS IN ℝ³ WITH INFINITELY MANY LIMIT CYCLES
• Limit cycles of resonant four-dimensional polynomial systems
• Bifurcation of limit cycles from a centre in ℝ⁴in resonance 1:N
• YET ANOTHER CHAOTIC ATTRACTOR
• Deterministic Nonperiodic Flow
• A NEW CHAOTIC ATTRACTOR COINED

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