Control of Chaos Dynamics in Jordan Recurrent Neural Networks

We propose two control methods of the Lyapunov exponents for Jordan-type recurrent neural networks. Both the two methods are formulated by a gradient-based learning method. The first method is derived strictly from the definition of the Lyapunov exponents that are represented by the state transition of the recurrent networks. The first method can control the complete set of the exponents, called the Lyapunov spectrum, however, it is computationally expensive because of its inherent recursive way to calculate the changes of the network parameters. Also this recursive calculation causes an unstable control when, at least, one of the exponents is positive, such as the largest Lyapunov exponent in the recurrent networks with chaotic dynamics. To improve stability in the chaotic situation, we propose a non recursive formulation by approximating ...