Artificial brain systems based on neural network discrete chaotic dynamics. Toward the development of conscious and rational robots

Mathematical models, which we claim can correspond to the discrete chaotic biochemical reaction dynamics of living and thinking systems, have been derived herein from first physicochemical principles and applied to neural network operations. In this application, we are assuming that the biochemical reactions are accompanied and controlled by an “information exchange” between neurons, neural networks and the different types of neural networks responsible for a brain’s various cognitive functions. Both the qualitative and quantitative meaning of “information” and “information exchange” between neural networks have been formulated in relation to a neuron’s chaotic states; we have formally introduced them into basic artificial neural network (ANN) equations. As will be shown in this work, each ANN uses a dynamic principle as a driving force that instantiates specific properties such as “self-organization” and “self-synchronization”. These result in the emergence of “phenomenological” states that form the complex patterns which we associate with brain consciousness, cognition and creativity. Our proposed ANN generates practically an unlimited variety of discrete time and space patterns which are controlled by the continuous parameters of the proposed mathematical models. It has provided us with the confidence that with ANN learning and training, we can fit the proper architectural and mathematical models to the desired cognitive and creative properties for an artificial intelligent autonomous system. Results of numerical simulations will be presented in a form of 2D and 3D discrete time-space distributed patterns. Application of the approach to the art of mandalas we argue can be extended to a proposed approach for autonomous robot path planning as presented and discussed in this chapter.