Many studies have failed to determine a systematic dose-response relationship across different cognitive tasks between caffeine and EEG power spectra. However, a nonlinear approach to EEG analysis, which reconstructs a multi-dimensional state space from each electrode recording, can be used to compute the number of active degrees of freedom in the signal (the correlation dimension, D2), and can be interpreted as a measure of signal complexity. This study attempted to determine a consistent dose-response relationship between caffeine and EEG D2, across six oral caffeine doses (100-600 mg), with each subject acting as their own control, to create a probabilistic bias against finding any consistent linear or nonlinear dose-response relationship across different cognitive tasks. The experiment (n = 10) was conducted with three within-subjects explanatory variables, 2 (experimental, placebo) x 8 (caffeine level) x 4 (type of cognitive task performed), with EEG D2 as the response variable, measured from Fz, F3, F4 and Cz. A significant three-way interaction was found [F(21,245.3) = 3.65, P = 0.001]. Regression analyses revealed a linear trend for the response variable across trials for the placebo condition (average R2 = 0.54), whereas linear+quadratic trends explained an average 30% of the variance for the experimental condition, compared to 0.01% for the linear fit, indicating a robust quadratic dose-response relationship between caffeine and EEG D2. Three conditions had positive quadratic co-efficients, and one condition had a negative quadratic co-efficient. These results are discussed in terms of the implications for brain dynamics, and with respect to recent criticisms of the computation of D2 from EEG.