Defective sleep arousal can contribute to significant sleep-related injuries and affect the quality of life. Investigating the arousal process is a challenging task as most of such events may be associated with subtle electrophysiological indications. Thus, developing an accurate model is an essential step toward the diagnosis and assessment of arousals. Here we introduce a novel approach for automatic arousal detection inspired by the states' recurrences in nonlinear dynamics. We first show how the states distance matrices of a complex system can be reconstructed to decrease the effect of false neighbors. Then, we use a convolutional neural network for probing the correlated structures inside the distance matrices with the arousal occurrences. Contrary to earlier studies in the literature, the proposed approach focuses on the dynamic behavior of polysomnography recordings rather than frequency analysis. The proposed approach is evaluated on the training dataset in a 3-fold cross-validation scheme and achieved an average of 19.20% and 78.57% for the area under the precision-recall (AUPRC) and area under the ROC curves, respectively. The overall AUPRC on the unseen test dataset is 19%.