Investigation of the determinism of complex dynamical systems using simple back propagation neural networks

Abstract

In this paper the deterministic manner of complex systems from which a time series of one variable is known, is investigated by the use of neural networks. The idea on which the method is based is that back propagation neural networks with sigmoid nodes can simulate deterministic systems. This means that when a neural network is able to learn a system successfully, the system is deterministic, but when it is not, no such statement can be directly asserted. In this case simple criteria are proposed, presuming that when the proper amount of information feeds the network its performance is improved. This improvement indicates the network's effort to capture, in some way, the deterministic properties of the simulated system. This consideration is confirmed by the observation that random systems do not satisfy any of the criteria proposed in this work. The neural method of investigating determinism is simpler than methods proposed in previous research work, since no pre-calculated parameter values, such as the delay time or the embedding dimension of the dynamical system, are necessary for its implementation.

Keywords:

• Neural networks
• Dynamical systems
• Chaos