Logical stochastic resonance in a nonlinear fractional-order system
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Logical stochastic resonance in a nonlinear fractional-order system Mingjie Hou1, Jianhua Yang1,2,a
, Shuai Shi1, Houguang Liu1
1 School of Mechatronic Engineering, China University of Mining and Technology, Xuzhou 221116,
People’s Republic of China
2 Jiangsu Key Laboratory of Mine Mechanical and Electrical Equipment, China University of Mining and
Technology, Xuzhou 221116, People’s Republic of China Received: 10 May 2020 / Accepted: 9 September 2020 © Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract We investigate logical stochastic resonance (LSR) in a nonlinear fractional-order system with an asymmetric bistable potential function. We use the success probability of the logical output to measure the logical operation ability of the system. If the success probability is 1, the logical output presents reliable LSR completely. When there are only two logical signals existing in the excitation, LSR can be realized by varying the value of the fractional order or the bias of the potential function. If the fractional order is relatively large, the system performs correct logical operations more easily. With the increase in the bias, the interval of the fractional order corresponding to LSR increases first and then decreases. When both logical signals and Gaussian white noise exist in the excitation, the intervals of the fractional order and the bias corresponding to LSR decrease with the increase in the noise intensity. In addition, with the increase in the value of the fractional order, the maximal value of the success probability also increases. Further, the system usually performs more accurate logical operations when the value of the fractional order lies in the interval [1, 1.5]. The results expand the achievements of LSR. They also provide a reference in choosing an optimal system of LSR.
1 Introduction Benzi proposed the concept of stochastic resonance (SR) when studying the cyclical change of the glaciers [1]. Since then, SR has been widely investigated in optical system [2], neuronal networks [3], polymer chain [4], Schmitt trigger [5], etc. These studies have shown the positive role of noise in the dynamical process. Murali et al. studied SR in the nonlinear system excited by noise and two logical signals [6]. They found that logical operations can be improved by an appropriate dose of noise. Based on this phenomenon, they put forward the concept of logical stochastic resonance (LSR) that is a new kind of SR. The success probability of the logical output is usually applied to measure the ability of the logical operation. With regard to LSR phenomenon, the success probability of the logical output increases to one and then decreases to zero with the noise intensity increasing gradually. Later, Murali et al. also realized LSR in circuits [7]. In many engineering fields, it is important to get reliable
a e-mail: [email protected] (corresponding author)
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Eur. Phys. J. Plus
(2020) 135:747
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