Fixed Attracting Closed Surfaces in Three and Higher Dimensional Dynamical Systems - Datta, Satadal; Bhattacharjee, Jayanta Kumar; Mukherjee, Dibya Kanti (Journal of Applied Nonlinear Dynamics, 2026)
Invariant tori (or ``fixed surfaces": attractors for neighboring periodic orbits in a dissipative dynamical system) have been widely studied but the corresponding generalization for quasi periodic orbits have rarely been discussed. Here we investigate ``higher dimensional fixed surfaces" by analyzing a pair of coupled non identical Van der Pol oscillators and also the Kuznetsov oscillator. We find that the renormalization group based approach introduced by Chen, Goldenfeld and Oono is ideally suited for analyzing the quasi periodic analogues of limit cycles. We also address entrainment issues in a pair of forced and coupled Van der Pol oscillators. Our principle finding there is that if two such independent oscillators one with frequency entrainment and the other without are coupled linearly, then it is possible to produce an entrained state via the coupling.