Design creativity is an inherently complex and recursive cognitive process involving nonlinear transitions between distinct cognitive states. This experimental neurocognitive study provides empirical support for theoretical nonlinear and recursive models of design creativity by examining neurocognitive processes across design creativity cognitive states, including idea generation (IDG), idea evolution (IDE), rating process (IDR), and rest mode (RST). EEG signals were recorded during loosely controlled design creativity tasks, and 13 well-established features were extracted from recurrence quantification analysis (RQA). A feature selection pipeline identified the most significant features for distinguishing between the cognitive states. Statistical analyses of the features provided deeper insights into brain dynamics and confirmed the significance of the selected features, supported by EEG topography maps. The findings revealed distinct and complex recursive dynamics across cognitive states, primarily involving the frontal, parietal and central regions, offering novel insights complementary to prior EEG studies. We also classified the cognitive states using the selected significant features through six classification models: k-Nearest Neighbor, Support Vector Machine, Naïve Bayes, Multi-Layer Perceptron, Linear Discriminant Analysis and Random Forest. To ensure robust evaluation, we applied three cross-validation strategies – hold-out, k-fold and one-subject-out – and combined the classifiers using majority voting fusion. Classification results (10-fold cross-validation) demonstrated high performance, with an average accuracy (96.23%), kappa (93.56%), recall (96.58%), precision (98.08%), F1-score (97.29%) and specificity (98.43%). The study provides findings that are consistent with theoretical expectations. Consistent with theoretical expectations, the findings deepen understanding of recursive and nonlinear neural dynamics in design creativity cognition and guide future research.