Center cyclicity of Lorenz, Chen and Lü systems

DOI10.1016/j.na.2019.06.012zbMath1428.37046OpenAlexW2950461812MaRDI QIDQ2007486

Douglas S. Shafer, Susanna Maza, Isaac A. García

Publication date: 21 November 2019

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/10459.1/66494

zbMATH Keywords

centerlimit cyclecenter manifoldcyclicity

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Bifurcations of singular points in dynamical systems (37G10) 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)

Related Items (8)

Local bifurcation and center problem for a more generalized Lorenz system ⋮ Weak Bi-Center and Bifurcation of Critical Periods in a Three-Dimensional Symmetric Quadratic System ⋮ Rigid centres on the center manifold of tridimensional differential systems ⋮ Bifurcation of limit cycles and isochronous centers on center manifolds for a class of cubic Kolmogorov systems in \(\mathbb{R}^3\) ⋮ The smallest bimolecular mass-action system with a vertical Andronov-Hopf bifurcation ⋮ Bifurcation of limit cycles and isochronous centers on center manifolds for four‐dimensional systems ⋮ Cyclicity of rigid centres on centre manifolds of three-dimensional systems ⋮ Hopf bifurcation in 3-dimensional polynomial vector fields

Cites Work

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• A classical approach to the analyticity problem of center manifolds
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• Cyclicity of polynomial nondegenerate centers on center manifolds
• Global dynamics of the generalized Lorenz systems having invariant algebraic surfaces
• Centers on center manifolds in the Lorenz, Chen and Lü systems
• Multiple Hopf bifurcation in \(\mathbb R^3\) and inverse Jacobi multipliers
• Inverse Jacobi multipliers
• The Center and Cyclicity Problems
• Heteroclinic bifurcations in a simple model of double-diffusive convection
• YET ANOTHER CHAOTIC ATTRACTOR
• Deterministic Nonperiodic Flow
• Ordinary Differential Equations with Applications
• A NEW CHAOTIC ATTRACTOR COINED
• Invariant algebraic surfaces of the Lorenz system
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