It is well known that linear vector fields defined in $\mathbb{R}^n$ can not have limit cycles, but this the case for other manifolds. We study existence of cycles bifurcating from a continuum periodic orbits on manifolds form $(\mathbb{S}^2)^m \times \mathbb{R}^n$ when such are perturbed inside class all fields. The done using averaging theory. also present an open problem concerning maximum n...

We study a model for cascade effects over finite networks based on a deterministic binary linear threshold model. Our starting point is a networked coordination game where each agent’s payoff is the sum of the payoffs coming from pairwise interactions with each of the neighbors. We first establish that the best response dynamics in this networked game is equivalent to the linear threshold dynam...