About Landau–Hopf scenario in a system of coupled self-oscillators

•We consider a network of five globally coupled Van der Pol oscillators.•We discussed Landau–Hopf scenario of successive birth of multi-frequency quasi-periodic motions.•We use the method of Lyapunov exponents.•We illustrate a birth of tori of increasing dimension via quasi-periodic Hopf bifurcations.

The conditions are discussed for which an ensemble of interacting oscillators may demonstrate the Landau–Hopf scenario of successive birth of multi-frequency quasi-periodic motions. A model is proposed that is a network of five globally coupled oscillators characterized by controlled degree of activation of individual oscillators. Illustrations are given for successive birth of tori of increasing dimension via quasi-periodic Hopf bifurcations.