Abstract
A system with an absolute nonlinearity is studied in this work. It is noted that the system is chaotic and has an adjustable amplitude variable, which is suitable for practical uses. Circuit design of such a system has been realized without any multiplier and experimental measurements have been reported. In addition, an adaptive control has been applied to get the synchronization of the system.
Highlights
Chaos in dynamic systems has been investigated for many years [1,2,3,4], new systems with chaos still attract the attention of numerous researches [5,6,7,8,9,10,11]
By using an absolute term, one of the most elementary chaotic systems was introduced by Linz and Sprott [21]
It is interesting that adjustable amplitude of chaotic attractor was obtained with absolute terms [28]
Summary
Chaos in dynamic systems has been investigated for many years [1,2,3,4], new systems with chaos still attract the attention of numerous researches [5,6,7,8,9,10,11]. It is worth noting that an absolute term is not a quadratic nonlinearity and can be implemented with diodes and operational amplifiers [22]. By using an absolute term, one of the most elementary chaotic systems was introduced by Linz and Sprott [21]. Such a system was realized by a circuit [22]. Authors investigated the synchronization of a chaotic system, which includes only four terms and an absolute-value nonlinearity [24]. Bao et al designed a memristor-based system with four line equilibria by implementing three absolute terms [27]. It is interesting that adjustable amplitude of chaotic attractor was obtained with absolute terms [28]
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