Attractor formation in dynamical systems with self-organising velocity fields

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The project will be devoted to the study of a special class of dynamical systems, in which the velocity fields are plastic and self-organising. Such systems have been recently proposed as mathematical prototypes of cognitive systems, which can automatically memorise and classify the incoming data without supervision and online. These systems respond to external stimuli by permanently modifying their velocity field, so that memories are created of groups of stimuli sharing some common properties. Memories can take the form of attractors, which can be of various kinds: from the simplest fixed points, through limit cycles, invariant tori and chaotic attractors. So far only the mechanisms for the formation of the simplest fixed-point attractors have been considered, while the discovery of the mechanisms for the spontaneous creation of more complex attractors remain a challenge. The project will aim at exploring the mathematical mechanisms behind the spontaneous formation of non-fixed-point attractors and of their basins in dynamical systems that learn by self-organising their velocity fields. The project fits within the University's Research challenge "Enabling Technologies", subsection "Intelligent Systems, Devices and Sensors" because it helps to pave the way to making intelligent devices based on the new physical principles, that would be different from those of classical or quantum computers, or neural networks.