Constructing the second order Poincaré map based on the Hopf-zero unfolding method

DOI10.1155/2013/294162zbMath1296.34119OpenAlexW2061739942WikidataQ58915847 ScholiaQ58915847MaRDI QIDQ2015330

Gen Ge, Wang Wei

Publication date: 23 June 2014

Published in: Abstract and Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2013/294162

zbMATH Keywords

normal form theory3D systemShilnikov homoclinicity

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Cites Work

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• Homoclinic and heteroclinic orbits in a modified Lorenz system
• High-order moments conservation in thermostatted kinetic models
• Breakdown of heteroclinic orbits for some analytic unfoldings of the Hopf-zero singularity
• \(n\)-dimensional stable and unstable manifolds of hyperbolic singular point
• Computation of the simplest normal form of a resonant double Hopf bifurcation system with the complex normal form method
• Local and global behavior near homoclinic orbits
• Global bifurcations and chaos. Analytical methods
• Elements of applied bifurcation theory.
• Bifurcation and chaos in the Duffing oscillator with a PID controller
• Constructing a new chaotic system based on the Šilnikov criterion
• Controllability of a nonholonomic macroeconomic system
• A perturbation method for computing the simplest normal forms of dynamical systems
• Complexity in the bifurcation structure of homoclinic loops to a saddle-focus