On stability of KIII model based on nonlinear dynamics

As a bionic system simulating biologic olfactory structure and characteristics, KIII model is different from traditional artificial neural networks on pattern recognition. But there is no quantificational index to judge the stability of KIII model. Based on nonlinear dynamics index, the problem is researched in this paper and a quantificational index, Lyapunov exponent, is used to judge the stability of KIII model. Three stages in pattern recognition process of KIII model are analyzed quantificationally using wolf method. The calculational results show that KIII model can change from chaotic stage to stable stage quickly and presents obvious synchronization stage, which is consistent with the analytic result drawn from phase graph. It is also shown that Lyapunov exponent is an effective method to judge the stability of KIII model.