Dissipative system with asymmetric interaction and Hopf bifurcation

Abstract

A dissipative system with asymmetric interaction, as well as the optimal velocity model, generally shows a Hopf bifurcation concerned with the transition from homogeneous motion to the formation of nontrivial patterns. We reveal that the origin of Hopf bifurcation in macroscopic phenomena is strongly related to asymmetric interaction in a microscopic many-body system, using the continuum system derived from the original discrete system.