Asymptotical stability of transiently chaotic neural networks

The asymptotic stability of transiently chaotic neural networks is considered in synchronously updating mode and asynchronously updating mode, where the connection matrix of the networks is asymmetric. By defining an energy function, we present several sufficient conditions which guarantee that the networks can asymptotically converge to a stable fixed point. These results improve and generalize some existing results in the previous references. Two numerical examples are given to illustrate the applicability of these conditions.