Stability of Periodic Orbits in the Averaging Theory: Applications to Lorenz and Thomas Differential Systems

DOI10.1142/S0218127418300070zbMath1388.34040WikidataQ130037513 ScholiaQ130037513MaRDI QIDQ4637649

Jaume Llibre, Murilo R. Cândido

Publication date: 25 April 2018

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

zbMATH Keywords

Lorenz systemaveraging theorycirculant systemstability of periodic orbitThomas system

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Stability of solutions to ordinary differential equations (34D20) Averaging method for ordinary differential equations (34C29)

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Cites Work

• Improving the averaging theory for computing periodic solutions of the differential equations
• New results on averaging theory and applications
• Qualitative dynamics from asymptotic expansions: Local theory
• Bifurcation of periodic orbits by perturbing high-dimensional piecewise smooth integrable systems
• A second order analysis of the periodic solutions for nonlinear periodic differential systems with a small parameter
• LABYRINTH CHAOS
• A Note on the Asymptotic Expansion of Eigenvalues
• Persistence of periodic solutions for higher order perturbed differential systems via Lyapunov–Schmidt reduction
• Higher order averaging theory for finding periodic solutions via Brouwer degree
• DETERMINISTIC CHAOS SEEN IN TERMS OF FEEDBACK CIRCUITS: ANALYSIS, SYNTHESIS, "LABYRINTH CHAOS"
• Averaging methods in nonlinear dynamical systems
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