Hopf Bifurcation in Symmetric Networks of Coupled Oscillators with Hysteresis

摘要: The standard approach to study symmetric Hopf bifurcation phenomenon is based on the usage of equivariant singularity theory developed by M. Golubitsky et al. In this paper, we present degree method which complementary approach. Our allows systematic problems in non-smooth/non-generic settings. exposition focused a network eight identical van der Pol oscillators with hysteresis memory, are coupled cube-like configuration leading S4-equivariance. memory source non-smoothness and presence an infinite dimensional phase space without local linear structure. Symmetric properties multiplicity bifurcating branches periodic solutions discussed context showing direct link between physical topology underlying problem.