It is a hot problem in epilepsy research to detect and predict seizures by EEG signals. Clinically, it is generally observed that there are only sudden abnormal signals during the ictal stage, but there is no significant difference in the EEG signal between the interictal and preictal stages. To solve the problem that preictal signals are difficult to recognize clinically, and then effectively improve the recognition efficiency of epileptic seizures, so, in this paper, some nonlinear methods are comprehensively used to extract the hidden information in the EEG signals in different stages, namely, phase space reconstruction (PSR), Poincaré section (PS), synchroextracting transform (SET) and machine learning for EEG signal analysis. Firstly, PSR based on C-C method is used, and the results show that there are different diffuse attractor trajectories of the signals in different stages. Secondly, the confidence ellipse (CE) is constructed by using the scatter diagram of the corresponding trajectory on PS, and the aspect ratio and area of the ellipse are calculated. The results show that there is an interesting transitional phenomenon in preictal stage. To recognize ictal and preictal signals, time-frequency (TF) spectrums which are processed by SET are fed into the convolutional neural networks (CNN) classifier. The accuracy of recognize ictal and preictal signals reaches 99.7% and 93.7% respectively. To summarize, our results based on nonlinear method provide new research ideas for seizures detection and prediction.