Non-Lipschitzian Approach to Discrete Event Dynamics
Complexity of dynamical system performance can be significantly enriched by exploiting a non-.
Non-Lipschitzian Approach↗
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Non-Lipschitzian neural dynamics
A novel approach is presented which is motivated by an attempt to remove one of the most fundamental limitations of artificial neural networks: their rigid behavior as compared with even the simplest biological systems. It is demonstrated that non-Lipschitzian dynamics, based on the faliure of the Lipschitz conditions at repellers, displays a new qualitative effect, i.e., a multichoice response to periodic external excitations. This makes it possible to construct unpredictable systems, represented in the form of coupled activation and learning dynamical equations. It is shown that unpredictable systems can be controlled by sign strings which uniquely define the system behavior by specifying the direction of the motions at the critical points. Unpredictable systems driven by sign strings are extremely flexible and can serve as a powerful tool for complex pattern recognition.
Barhen, Jacob↗
Creative-Dynamics Approach To Neural Intelligence
Paper discusses approach to mathematical modeling of artificial neural networks exhibiting complicated behaviors reminiscent of creativity and intelligence of biological neural networks. Neural network treated as non-Lipschitzian dynamical system - as described in "Non-Lipschitzian Dynamics For Modeling Neural Networks" (NPO-17814). System serves as tool for modeling of temporal-pattern memories and recognition of complicated spatial patterns.
Zak, Michail A.↗
An unpredictable-dynamics approach to neural intelligence
The theoretical basis for a dynamic neural network architecture that takes advantage of the notion of terminal chaos to process information in a way that is phenomenologically similar to brain activity is presented. The architecture exploits the phenomenology of nonlinear dynamic systems as an alternative to the traditional paradigm of finite-state machines. It is based on some effects of non-Lipschitzian dynamics. The nonlinear phenomenon of terminal chaos and its relevance to brain activity are examined.
Zak, Michail↗