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Nontrivial Attractors of the Perturbed Nonlinear Schrödinger Equation: Applications to Associative Memory and Pattern Recognition
Author(s) -
Cherny Valentin V.,
Byrnes Tim,
Pyrkov Alexey N.
Publication year - 2019
Publication title -
advanced quantum technologies
Language(s) - English
Resource type - Journals
ISSN - 2511-9044
DOI - 10.1002/qute.201800087
Subject(s) - attractor , dissipative system , content addressable memory , nonlinear system , soliton , physics , perturbation (astronomy) , hopfield network , amplitude , nonlinear schrödinger equation , dissipative soliton , dynamical systems theory , phase space , classical mechanics , mathematical analysis , artificial neural network , mathematics , quantum mechanics , computer science , machine learning
Computers are dynamical systems that carry out information processing through their change of state with time. For instance, neural networks such as Hopfield's associative memory are dissipative dynamical systems in a finite dimensional configuration space with attractors that represent stored patterns. In particular, dissipative dynamical systems with an infinite dimensional configuration space are of broad interest and have the possibility to store and restore complex and strongly distorted data structures. In this work, the nonlinear Schrödinger equation (NLSE) with a dissipative perturbation which creates a frictional force acting on soliton is considered. It is shown that the control of the perturbative term allows one to decrease the velocity of soliton to zero and conserve a positive value of its amplitude. The existence of such a frictional force would suggest that the perturbation makes the zero‐velocity solitonic solution of non‐zero amplitude into an attractor for all evolution trajectories whose initial conditions are moving solitons. This allows a way to store information in the infinite dimensional dynamical system governed by NLSE using principles which are completely analogous to that of Hopfield's associative memory. This approach can be realized with solitons in Bose–Einstein condensates and nonlinear optical systems.