Dynamics of a ring of three unidirectionally coupled Duffing oscillators with time-dependent damping

We study dynamics of a ring three unidirectionally coupled double-well Duffing oscillators for different values the damping coefficient: fixed dumping, proportional to time, and inversely time. The in all cases is analyzed through time series, Fourier Hilbert transforms, Poincar\'e sections, as well bifurcation diagrams Lyapunov exponents with respect coupling strength. In first case, we observe well-known route from stable steady state hyperchaos Hopf series torus bifurcations, strength increased. second system highly dissipative converges into one equilibria. Finally, third transient toroidal takes place.