With the rapid development of emitter individual identification technology in cognitive radio networks, electromagnetic emitter individual target identification based on deep learning has received much attention. However, the confusion of unintentional features (i.e., individual fingerprint features) and modulation features resulting from the received signal might lead to low identification accuracy. In order to address this narrow, we propose an emitter individual identification network based on the competitive collaboration framework, called Specific Emitter Identification with Adaptive Decomposition and Extraction of individual fingerprint features (SEI-ADE), which can adaptively decompose and extract individual fingerprint features. Firstly, a signal adaptive decomposition network is proposed to distinguish the emitter signal and the interference signal by adopting the gradient inversion layer and the non-sequential characteristics of the signal. Then, in order to distinguish and extract corresponding features, the feature extractor and the training loss constraints are constructed for individual fingerprint feature signals, modulation signals, and external emitter interference signals, respectively. The proposed framework can continuously adjust the gradient loss, classification loss, and timing coding contrast loss, thus minimizing the entire training loss. For the separation of the modulation signal and individual fingerprint feature signal, the signal is transformed into the feature domain, and a mask prediction network is proposed to locate the domain of the individual fingerprint feature. The obtained experimental results show the outstanding performance of our proposal, compared with the current benchmarks. All our models and code are available at https://github.com/jn-z/SEI-ADE.