Limit cycles bifurcating from a zero-Hopf equilibrium of a 3-dimensional continuous differential system

DOI10.1007/s40863-021-00212-9zbMath1477.37061OpenAlexW3130258069WikidataQ107169757 ScholiaQ107169757MaRDI QIDQ2042190

Jaume Llibre, Sara Kassa, Amar Makhlouf

Publication date: 28 July 2021

Published in: São Paulo Journal of Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://ddd.uab.cat/record/239769

zbMATH Keywords

limit cycleperiodic orbitaveraging theoryzero-Hopf bifurcationzero-Hopf equilibriumcontinuous differential system

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Averaging method for ordinary differential equations (34C29) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Stability theory for smooth dynamical systems (37C75)

Related Items (1)

Limit cycles of polynomial differential systems of degree 1 and 2 on the cylinder

Cites Work

• Unnamed Item
• Zero-Hopf bifurcation in the generalized Michelson system
• On Yu. A. Mitropol'skii's theorem on periodic solutions of systems of nonlinear differential equations with nondifferentiable right-hand sides
• Detecting periodic orbits in some 3D chaotic quadratic polynomial differential systems
• Nonlinear differential equations and dynamical systems
• Averaging methods for finding periodic orbits via Brouwer degree.
• A novel chaotic system without equilibrium: dynamics, synchronization, and circuit realization
• Elementary quadratic chaotic flows with no equilibria
• Averaging methods in nonlinear dynamical systems

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