Diffusion dynamics near critical bifurcations in a nonlinearly damped pendulum system

We numerically study the diffusion dynamics near critical bifurcations such as sudden widening of the size of a chaotic attractor, intermittency and band-merging of a chaotic attractor in a nonlinearly damped and periodically driven pendulum system. The system is found to show only normal diffusion. Near sudden widening and intermittency crisis power-law variation of diffusion constant with the control parameter ω of the external periodic force f sin ωt is found while linear variation of it is observed near band-merging crisis. The value of the exponent in the power-law relation varies with the damping coefficient and the strength of the added Gaussian white noise.

► Nonlinearly damped and periodically driven pendulum system shows normal diffusion alone.
► Near sudden widening and intermittency crises power-law variation of diffusion constant occurs.
► Linear variation of diffusion constant is observed near band-merging crisis.
► The exponent value in the power-law varies with the strength of the added noise.