Abstract
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.
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References
Brandt L (1957) The π-theorem of the theory of dimensionality. Arch Ration Mech Anal 1:35
Brillouin L (1962) Science and information theory. Academic, New York
Gontar V (1993) New theoretical approach for physicochemical reactions dynamics with chaotic behavior. In: Field RJ, Györgyi L (eds) Chaos in chemistry and biochemistry. World Scientific, Singapore
Gontar V (1995) Calculus of iterations and dynamics of physicochemical reactions. Math Comput Simul 39:603–608
Gontar V (1997) Theoretical foundation for the discrete chaotic dynamics of physicochemical systems: chaos, self-organization, time and space in complex systems. Discret Dyn Nat Soc 1(1):31–43
Gontar V (2000a) Entropy as a driving force for complex and living systems dynamics. Chaos Soliton Fract 11:231–236
Gontar V (2000b) Theoretical foundation of Jung’s “Mandala Symbolism” based on discrete chaotic dynamics of interacting neurons. Discret Dyn Nat Soc 5:1
Gontar V (2004) The dynamics of living and thinking systems, biological networks, and the laws of physics. Discret Dyn Nat Soc 8:2
Gontar V (2007) Some creative properties of the 2D and 3D lattice distributed interconnected chaotic oscillators and neuronal networks. PAMM 7:2030047–2030048
Gontar V, Grechko O (2006) Generation of symmetrical colored images via solution of the inverse problem of chemical reactions discrete chaotic dynamics. Int J Bifurcation Chaos 16:5
Gontar V, Grechko O (2007) Mathematical imaging using discrete chemical reactions dynamics. Fractals 15:4
Gontar V, Tkachenko C (2012) Autonomous robot path planning algorithm based on neural network discrete chaotic dynamics. Math Model 7:1
Grechko O, Gontar V (2009) Visual stimuli generated by biochemical reactions discrete chaotic dynamics as a basis for neurofeedback. J Neurother 13:1
Haykin SO (1998) Neural networks: a comprehensive foundation. Prentice Hall, Englewood Cliffs
Jung CG (1973) Mandala symbolism. Princeton University Press, Princeton
Shannon CE (1948) A mathematical theory of communication. Bell Syst Tech J 27(3):379–423
Wolfram SA (2002) New kind of science. Wolfram Media, Champaign
Acknowledgment
I would like to express my special thanks to Prof. William Lawless for fruitful critiques and discussions about the topic and for help in editing this manuscript.
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Gontar, V. (2016). Artificial Brain Systems Based on Neural Network Discrete Chaotic Dynamics. Toward the Development of Conscious and Rational Robots. In: Mittu, R., Sofge, D., Wagner, A., Lawless, W. (eds) Robust Intelligence and Trust in Autonomous Systems. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-7668-0_6
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DOI: https://doi.org/10.1007/978-1-4899-7668-0_6
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