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arXiv:2210.00970 · Condensed Matter Physics

Chaos synchronization in a BEC system using fuzzy logic controller

Eren Tosyalı, Yeşim Öniz, F. Aydogmus Sen

Published Jan 1, 2022• 0 citations
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Abstract

Since the presence of chaos in Bose-Einstein condensate (BEC) systems plays a destructive role that can undermine the stability of the condensates, controlling the chaos is of great importance for the creation of the BEC. In this paper, a fuzzy logic controller (FLC) to synchronize the chaotic dynamics of two identical master-slave BEC systems has been proposed. Unlike the conventional approaches, where expert knowledge is directly used to construct the fuzzy rules and membership functions, the fuzzy rules have been constructed using Lyapunov stability theorem ensuring the synchronization process. The effectiveness of the proposed controller has been demonstrated numerically.

DOI
10.5488/cmp.25.33501

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Since the presence of chaos in Bose-Einstein condensate (BEC) systems plays a destructive role that can undermine the stability of the condensates, controlling the chaos is of great importance for the creation of the BEC. In this paper, a fuzzy logic controller (FLC) to synchronize the chaotic dynamics of two identical master-slave BEC systems has been proposed. Unlike the conventional approaches, where expert knowledge is directly used to construct the fuzzy rules and membership functions, the fuzzy rules have been constructed using Lyapunov stability theorem ensuring the synchronization process. The effectiveness of the proposed controller has been demonstrated numerically.
Abstract Due to the difficulty of studying nonlinear quantum systems and the unique composition of Bose–Einstein condensate (BEC) systems, BECs face significant difficulties in solving dynamic analysis and chaotic control problems. Therefore, Hartree–Fock mean field theory is introduced to study the chaotic characteristics, control, and synchronization issues of BEC systems loaded on optical lattices. First, the stability and chaos of BECs in optical lattices were analyzed. Subsequently, constant shift method and activation control were introduced based on the Gross–Pitaevskii equation to achieve control and synchronization of the BEC system. Second, based on the Lyapunov exponent theory, offset parameters are added to BEC chaotic control to achieve control of particle density. Finally, based on the stability theory of linear systems, a control term is introduced to achieve variable analysis of the system’s drive–response system, ensuring that chaotic systems with different initial conditions can still achieve good synchronization and anti-synchronization control. The chaotic problem of BEC system was analyzed using numerical and theoretical methods in the experiment. The effect of adjusting the parameters of the BEC system under the constant shift method is significant. The system exhibits a chaotic state under the Lyapunov exponent, which is mainly concentrated between [3.4, 4.5], demonstrating good system stability. When the offset constant range is [4.21, 5.67], the maximum Lyapunov exponent value is below 0. In the problem of chaotic synchronization, adding activation control causes the system’s time series to exhibit anti-synchronization with spatiotemporal variable variation, while adding control terms leads the system to tend towards synchronization and anti-synchronization with time evolution. The analysis of chaotic control problems in BEC systems can provide reference value and theoretical basis for the dynamic research of quantum physics and related nonlinear systems.
Chaos control of a Bose–Einstein condensate (BEC) loaded into a moving optical lattice with attractive interaction is investigated on the basis of Lyapunov stability theory. Three methods are designed to control chaos in BEC. As a controller, a bias constant, periodic force, or wavelet function feedback is added to the BEC system. Numerical simulations reveal that chaotic behavior can be well controlled to achieve periodicity by regulating control parameters. Different periodic orbits are available for different control parameters only if the maximal Lyapunov exponent of the system is negative. The abundant effect of chaotic control is also demonstrated numerically. Chaos control can be realized effectively by using our proposed control strategies.