Equivariant bifurcations in a non-local model of ferromagnetic materials

In this work we study the bifurcations from the trivial equilibrium of the equation ∂u∂t(x,t)=−u(x,t)+tanh(β(J∗u)(x,t)), in the space of 2τ periodic functions. This is accomplished with the help of the equivariant branching lemma, which allows us to take into account the symmetries present in the model. We show that the phenomenon of 'spontaneous symmetry-breaking' occurs here, that is, the bifurcating solutions are less symmetric than the trivial one. We also prove that, under certain conditions, these equilibria can be globally continued.