Imperfect Bifurcation in Structures and Materials: Engineering Use of Group-Theoretic Bifurcation Theory. Applied Mathematical Sciences, Vol 149

Imperfection sensitivity of hilltop branching points of systems with dihedral group symmetry

“…A theoretical tool to describe a system invariant with respect to a dihedral group is presented as a summary of [33].…”

“…The group-theoretic multiple points were studied by group-theoretic bifurcation theory, which is a standard strategy to describe qualitative aspects of bifurcation of symmetric systems [30][31][32][33]. The group-theoretic study of bifurcation, despite its completeness, is not necessarily common in structural engineering.…”

“…The bifurcation of a system with regular-polygonal symmetry, the most common symmetry in structures, has been studied extensively [30,31,[33][34][35][36][37][38][39]. Generically critical points of this system are either, a limit point of loading parameter, a simple bifurcation point, or a double bifurcation point.…”

Exact multiplicity of solutions to perturbed logistic type equations on a symmetric domain

“…Singularity theory and perturbation theory have been used in discussion of such imperfect bifurcation phenomena, see [1][2][3]. In [4,5], we developed a theory of imperfect bifurcation theory in infinite dimensional spaces based on implicit function theorem and its variants including saddle-node, transcritical and pitchfork bifurcation theorems proved in [6,7].…”

Numerical Simulations of Imperfect Bifurcation of Jet in Crossflow

“…These perturbations make the practical model and the numerical model slightly different to the ideal model, which is named imperfections. The bifurcation caused by imperfections is named imperfect bifurcation (Ikeda and Murota, 2010). The structural stability of a dynamic system can be analyzed using the Andronov and Pontryagin theorem which can be given as follows (Kuznetsov, 1998 Fig.8a shows a local view of the limiting streamline pattern adjacent to the cooling hole in the case of M=0.5 and the corresponding topological structure.…”