Coupled Oscillatory Systems with 𝔻4 Symmetry and Application to van der Pol Oscillators

DOI10.1142/S0218127416501418zbMath1345.34060MaRDI QIDQ2819435

Pei Yu, Adrian C. Murza

Publication date: 29 September 2016

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

zbMATH Keywords

periodic solutionsHopf bifurcationdihedral groupvan der Pol oscillatorheteroclinic cyclesspatio-temporal symmetry

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Symmetries, invariants of ordinary differential equations (34C14) Bifurcation theory for ordinary differential equations (34C23) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Dynamical aspects of symmetries, equivariant bifurcation theory (37G40) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (1)

Noninvasive Stabilization of Periodic Orbits in O4-Symmetrically Coupled Systems Near a Hopf Bifurcation Point

Cites Work

• Dynamics of two van der Pol oscillators coupled via a bath
• Spectral sequences and parametric normal forms
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Coupled van der Pol oscillators. A model of excitatory and inhibitory neural interactions
• Singularities and groups in bifurcation theory. Volume II
• The symmetry perspective. From equilibrium to chaos in phase space and physical space
• A Bifurcation Approach to the Synchronization of Coupled Van der Pol Oscillators
• Permissible symmetries of coupled cell networks
• Asymptotic stability of heteroclinic cycles in systems with symmetry
• SIMPLEST NORMAL FORMS OF HOPF AND GENERALIZED HOPF BIFURCATIONS
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