Enhanced confinement regimes (H-mode) in tokamak plasmas are accompanied by pulses of energy and particle release known as edge localised modes (ELMs). The characteristics of ELMs, and their control, are central topics for ITER. Theories exist for some elements of the ELMing process, but there is no first principles model incorporating all the relevant physical effects. ELM categorisation is phenomenological, and few papers have addressed ELM sequences as the pulsed outputs of a nonlinear system. Characterisation of ELMing processes by applying dynamical systems theory to the data, as here, strengthens the scientific basis for understanding, prediction, and control. We construct delay plots for the measured time intervals between successive ELMs in six similar plasmas in the JET tokamak. This set includes JET Pulse No: 57865, where the H-mode closely approaches an ITER operating regime with respect to some key dimensionless parameters. We find that type I ELMing in these plasmas exhibits transitions dependent on the gas puffing rate as control parameter. In all six JET plasmas, the toroidal magnetic field density is 2.7T, the plasma current is 2.5MA, neutral beam and ion cyclotron resonance heating power are 13.5MW and 2.0MW respectively, and the H98 confinement factor is 0.87­1.0. Gas puffing terminates at 23.3s and neutral beam heating is ramped down from 23.5 to 24.5s. The differences in type I ELM character are largely determined by the different levels of externally applied gas puffing. The intensity of the Da signal, which sometimes saturates, is not necessarily a proxy for the magnitude of the underlying ELM plasma phenomenon. However occurrence times, and hence inter-ELM time intervals, are well defined. The occurrence time of each ELM is inferred from the Da datasets using an algorithm similar to Ref.[5], which exploits the steep leading edge of each ELM. This generates a sequence of event times tn for each nth ELM, and hence inter-event times dtn = tn ­ tn­1. These sequences are used to construct delay plots, which capture key aspects of the phase space evolution of the plasma physics system responsible for ELMing.