Dynamics of three Toda oscillators with nonlinear unidirectional coupling

We study the dynamics of three unidirectionally coupled Toda oscillators with nonlinear coupling function in the form of first three terms of Taylor power series. We analytically investigate how the coupling influence the stability of steady state. Basing on calculation of the first Lyapunov coefficient, we show that destabilization may occur by the sub- or supercritical Andronov-Hopf bifurcation. Born periodic solutions are calculated using path-following as a function of coupling strength and Taylor series coefficients. We present that initially stable or unstable branch of periodic solutions may undergo a sequence of bifurcations including: period doubling, Neimark-Saker and fold