The cocktail party phenomenon describes the ability of the human brain to focus auditory attention on a particular stimulus while ignoring other acoustic events. Selective auditory attention detection (SAAD) is an important issue in the development of brain-computer interface systems and cocktail party processors. This paper proposes a new dynamic attention detection system to process the temporal evolution of the input signal. In the proposed dynamic system, after preprocessing of the input signals, the probabilistic state space of the system is formed. Then, in the learning stage, different dynamic learning methods, including recurrent neural network (RNN) and reinforcement learning (Markov decision process (MDP) and deep Q-learning) are applied to make the final decision as to the attended speech. Among different dynamic learning approaches, the evaluation results show that the deep Q-learning approach (MDP+RNN) provides the highest classification accuracy (94.2%) with the least detection delay. The proposed SAAD system is advantageous, in the sense that the detection of attention is performed dynamically for the sequential inputs. Also, the system has the potential to be used in scenarios, where the attention of the listener might be switched in time in the presence of various acoustic events.