Haopin Wu | Searcharxiv

arXiv2018

Nonlinear Vibrations in the Fullerene Molecule $C_{60}$

In this paper we analyze nonlinear dynamics of the fullerene molecule. We prove the existence of global branches of periodic solutions emerging from an icosahedral equilibrium (nonlinear normal modes). We also determine the symmetric properties of the branches of nonlinear normal modes for maximal orbit types. We find several solutions which are standing and rotating waves that propagate along the molecule with icosahedral, tetrahedral, pentagonal and triangular symmetries. We complement our theoretical results with numerical computations using Newton's method.

math.DS↗

arXiv2016

Bifurcation of space periodic solutions in symmetric reversible FDEs

In this paper, we propose an equivariant degree based method to study bifurcation of periodic solutions (of constant period) in symmetric networks of reversible FDEs. Such a bifurcation occurs when eigenvalues of linearization move along the imaginary axis (without change of stability of the trivial solution and possibly without $1:k$ resonance). Physical examples motivating considered settings are related to stationary solutions to PDEs with non-local interaction: reversible mixed delay differential equations (MDDEs) and integro-differential equations (IDEs). In the case of $S_4$-symmetric networks of MDDEs and IDEs, we present exact computations of full equivariant bifurcation invariants. Algorithms and computational procedures used in this paper are also included.

math.DS↗