Neimark Sacker bifurcations and non-linear energy exchange in chains of non-linear oscillators

We treat a chain of oscillators with linear stiffness and internal external cubic non-linearities. The method harmonic balance is used to determine the non-linear modes Hamiltonian system. For each equilibrium point, stability analysis performed by means associated monodromy matrix. numerical results shows that branch points, limit points Neimark–Sacker bifurcations exist in aim paper study how they drive energy system: make transfer between possible, while can lead chaotic behaviour. As number increases, required reach first bifurcation follows remarkable regularity.