A limit cycle problems of BSB model with delay

In this paper we discuss the limit cycle property of a family of Brain-state-in-a-Box (BSB) models with delay. The dynamics of the model is addressed using analysis method. For the network with arbitrary weight matrix, the conditions for the existence of cycle of length 2 are presented. The advantage of the method is the ability to be predicted limit cycles in updating initial three steps. At last, the testing result demonstrates that theoretical analysis are correct.