Home > Archives > Additional Archives > Vladimir Gontar   Vladimir Gontar Director, Int. Group for Chaos Studies Ben-Gurion University of the Negev galita@bgumail.bgu.ac.il http://www.bgu.ac.il/chaos/ From Discrete Chaotic Dynamics of  Living and Thinking Systems to a New Generation of Neural Networks and "Artificial Brain"   The monopoly of differential equations for describing all kinds of natural and social systems dynamics was broken by the results obtained in chaos studies. It is became clear that difference equations /iterations/ can generate all types of complex systems dynamics. But the absence of the general rules and physical principles, which should lead us to the construction of difference equations /as it have been done from the very beginning with differential equations/ make this discrete calculus not so widely used as it could be. Our main aim is to elaborate rules and first principles for the construction of systems of difference equations describing the spatial-temporal dynamic behavior of the processes similar to ones ruling the construction of systems of ordinary and partial differential equations. This aim requires a clarification of the meaning of discrete space and time, continuity and discreteness, determinism and randomness. As one of the possible approaches for the construction from the first principles basic equations in a form of iterations connected we will consider discrete physicochemical reactions dynamics [1]. These dynamics are based on entropy principle of extremality, p -theorem of the theory of dimensionality, and leads to systems of non-linear iterations. On that bases we will discuss calculus of iterations, discrete chaotic dynamics paradigm and its application for mathematical modeling of complex, living and thinking systems [2,3]. Applications of the presented discrete chaotic dynamics mathematical models for image and signal processing, new generation of neural networks and "artificial brain" will be presented. References 1. V. Gontar, "Calculus of iterations and dynamics of physicochemical reactions" Mathematics and Computers in Simulation, , 39, (1995), pp. 603-609 2. V.Gontar, "Discrete dynamics for mathematical simulation of living systems", Chaos, Solitons and Fractals, 8, No.4, (1997) pp.517-524 3. V. Gontar, "Theoretical foundation of Jung’s Mandala Symbolism based on discrete chaotic dynamics of interacting neurons" Discrete Dynamics In Nature and Society, 5, No.1, (2000), pp.19-28 Some relevant information could be found on http://www.bgu.ac.il/chaos
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