This research attempts to identify and model ways to store information in dynamic, chaotic neural networks. The justification for this research is given by both biological as well as theoretical motivations [2, 27, 29, 46, 60, 107]. Firstly, there seems to be substantial support for the use of dynamic networks to study more complex and interesting behaviour. The artificial neural networks (ANN) have specific properties that define its order, such as size, type and function. Simply extending the ANN with complex non linear dynamics does not improve the memory performance of the network, it modifies the rate at which a global minimum may be located, if such .a state exists. Using non-linear differential equations may add more com plexity to the system and thereby increase the possible memory states. Secondly, even though chaos is generally undesirable, it has important properties that may be exploited to store and retrieve information [98]. These are the space filling, the possibility of control via delayed feedback, synchronization and the sensitive dependence on initial conditions. It is demonstrated in this thesis that by using delayed feedback, Unsta ble Periodic Orbits (UPO) may be stabilized to reduce the complexity of a chaotic system to n-periodic behaviour. This is a well known effect of de layed control in many types of chaotic models (e.g. Rossler equation), and the periodicity of the resulting orbit is determined by the model parameter as well as the delay (T) and the feedback strength (K) of the control func tion (F). Even though a theoretical infinite number of UPOs exist within a chaotic attractor only some can practically be stabilized. Furthermore, it is shown that input added to the delayed feedback controlled system allows different orbits to be stabilized. The addition of multiple delays changes the number and types of orbits that are available for stabilization. The use of synchronization between similar sets of chaotic systems may be used to target specific orbits.
Olde Scheper, Tjeerd
Year: 2002
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