The aim of this study is to implement an automatic system to detect the activation phases of Cyclic Alternating Pattern (CAP). CAP is a sleep phenomenon composed of consecutive sequences of activations and non-activations observed during the sleep time. Statistical Behavior of Local Extrema (SBLE) method is used for feature extraction and similarity index is used for decision making. SBLE is a symbolic technique that can characterize behavior of chaotic signals. The C4-A1 EEG lead of six healthy adult subjects was used. SBLE features are extracted from delta EEG band. By using this method and second by second comparison output of the system with sleep expert visual scoring, sensitivity of 75.83%, specificity of 81.30% and accuracy of 80.51% is achieved.