Equivariant Hopf bifurcation with general pressure laws

•We find a new class of examples of equivariant Hopf bifurcations.•Our examples are from systems of PDEs and include two bifurcation parameters.•The dynamics are connected with properties of hyperbolic conservation laws.•The convexity of pressure has no influence on the stability of bifurcated waves.

The equivariant Hopf bifurcation dynamics of a class of system of partial differential equations is studied. The connections between the current dynamics and fundamental concepts in hyperbolic conservation laws are explained. The unique approximation property of center manifold reduction function is used in the current work to determine certain parameter in the normal form. The current work generalizes the study of the second author (J. Yao, 2014) and discovers a class of examples of O(2)O(2) Hopf bifurcation with two parameters arising from systems of partial differential equations.