ANALYSIS OF THE T-POINT–HOPF BIFURCATION WITH ℤ2-SYMMETRY: APPLICATION TO CHUA'S EQUATION

DOI10.1142/S0218127410026265zbMath1193.34078OpenAlexW2000074848MaRDI QIDQ3586827

Fernando Fernández-Sánchez, Antonio Algaba, Manuel Merino, Alejandro J. Rodríguez-Luis

Publication date: 1 September 2010

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

Full work available at URL: https://doi.org/10.1142/s0218127410026265

zbMATH Keywords

Hopf bifurcationglobal bifurcationsT-pointChua's equation\(\mathbb Z_{2}\)-symmetry

Mathematics Subject Classification ID

Symmetries, invariants of ordinary differential equations (34C14) Bifurcation theory for ordinary differential equations (34C23) Dynamical aspects of symmetries, equivariant bifurcation theory (37G40) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Complex behavior and chaotic systems of ordinary differential equations (34C28) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Hyperbolic singular points with homoclinic trajectories in dynamical systems (37G20)

Related Items (3)

Analysis of the T-point-Hopf bifurcation in the Lorenz system ⋮ Experimentally Accessible Orbits Near a Bykov Cycle ⋮ HOMOCLINIC INTERACTIONS NEAR A TRIPLE-ZERO DEGENERACY IN CHUA'S EQUATION

Cites Work

• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• T-points: A codimension two heteroclinic bifurcation
• On systems with separatrix contour containing two saddle-foci.
• Functional equations and conjugacy of local diffeomorphisms of a finite smoothness class
• The bifurcations of separatrix contours and chaos
• A model for the analysis of the dynamical consequences of a nontransversal intersection of the two-dimensional manifolds involved in a T-point
• T-points in a \(\mathbb Z_2\)-symmetric electronic oscillator. I: Analysis
• Accumulations of \(T\)-points in a model for solitary pulses in an excitable reaction-diffusion medium
• The non-transverse Shil'nikov-Hopf bifurcation: uncoupling of homoclinic orbits and homoclinic tangencies
• Nontransversal curves of \(T\)-points: A source of closed curves of global bifurcations
• Analysis of the T-point-Hopf bifurcation
• New aspects in the unfolding of the nilpotent singularity of codimension three
• LORENZ EQUATION AND CHUA’S EQUATION
• OPEN-TO-CLOSED CURVES OF SADDLE-NODE BIFURCATIONS OF PERIODIC ORBITS NEAR A NONTRANSVERSAL T-POINT IN CHUA'S EQUATION
• SOME RESULTS ON CHUA'S EQUATION NEAR A TRIPLE-ZERO LINEAR DEGENERACY
• CLOSED CURVES OF GLOBAL BIFURCATIONS IN CHUA'S EQUATION: A MECHANISM FOR THEIR FORMATION
• BI-SPIRALING HOMOCLINIC CURVES AROUND A T-POINT IN CHUA'S EQUATION
• Chaotic dynamics in ${\mathbb Z}_2$-equivariant unfoldings of codimension three singularities of vector fields in ${\mathbb R}^3$
• Cocoon bifurcation in three-dimensional reversible vector fields

This page was built for publication: ANALYSIS OF THE T-POINT–HOPF BIFURCATION WITH ℤ₂-SYMMETRY: APPLICATION TO CHUA'S EQUATION