Chaos in Born-Infeld-AdS black hole within extended phase space

Born-Infeld-AdS black holes in extended phase space may possess phase structures resembling that of van derWaals fluid in four-dimensional spacetime. We study dynamics of its state, which is in the unstable spinodal region initially on phase space, under time-periodic thermal perturbations. By applying theMelnikovmethod, it is found that there exists a critical amplitude gamma(c) of the perturbations, which depends on the Born-Infeld parameter b and the black hole charge Q, such that chaos occurs for gamma > gamma(c). We found that larger b or Q makes the onset of chaos easier. Space-periodic thermal perturbations on its equilibrium state are also studied and there is always chaos for whatever the perturbation amplitude is.