We study persistence of periodic solutions perturbed slowly varying discontinuous differential equations assuming that the unperturbed (frozen) equation has a non singular solution. The results this paper are motivated by result Holmes and Wiggins where authors considered two dimensional Hamiltonian family smooth systems depending on scalar variable which is solution singularly equation.

We provide linear approximations to the marginal distributions for a class of infinite-state continuous-time stationary Markov chains in slowly varying environents. We take an approach motivated by light-traffic approximations to stationary point processes, which permits us to consider general stationary environments. Under mild assumptions we show that Jackson networks with routing not affecte...

We study a linear stochastic approximation algorithm that arises in the context of reinforcement learning. The algorithm employs a decreasing step-size, and is driven by Markov noise with time-varying statistics. We show that under suitable conditions, the algorithm can track the changes in the statistics of the Markov noise, as long as these changes are slower than the rate at which the step-s...

A Popov criterion is derived for systems with slowly timevarying parameters. The parameters and their time derivatives are assumed to take values in convex polytopes.