We study the bifurcations of slow-fast cycles with two canard points in singularly perturbed planar systems. After analyzing local dynamics lying on S-shaped critical manifolds, we give a sufficient condition under which there exist three hyperbolic limit bifurcating from some cycles. The proof is based geometric singular perturbation theory. Then, apply results to cubic Liénard equations quadr...

We substantially extend our relaxation theory for perturbed many-body quantum systems from [Phys. Rev. Lett. 124, 120602 (2020)] by establishing an analytical prediction the time-dependent observable expectation values which depends on only two characteristic parameters of perturbation operator: its overall strength and range or band width. Compared to previous theory, a significantly larger st...