Initial offset boosting coexisting attractors in memristive multi-double-scroll Hopfield neural network
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ORIGINAL PAPER
Initial offset boosting coexisting attractors in memristive multi-double-scroll Hopfield neural network Sen Zhang · Jiahao Zheng · Xiaoping Wang Zhigang Zeng · Shaobo He
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Received: 18 June 2020 / Accepted: 8 October 2020 © Springer Nature B.V. 2020
Abstract Memristors are widely considered to be promising candidates to mimic biological synapses. In this paper, by introducing a non-ideal flux-controlled memristor model into a Hopfield neural network (HNN), a novel memristive HNN model with multidouble-scroll attractors is constructed. The parity of the number of double scrolls can be flexibly controlled by the internal parameters of the memristor. Through theoretical analysis and numerical simulation, various coexisting attractors and amplitude control are observed. Particularly, the interesting and rare phenomenon of the memristor initial offset boosting coexisting dynamics is discovered, in which the initial offset boosting coexisting double-scroll attractors with banded attraction basins are distributed in a line along the boosting route with the variation of the memristor initial condition. S. Zhang Institute of Artificial Intelligence, School of Artificial Intelligence and Automation and the Key Laboratory of Image Processing and Intelligent Control of Education Ministry of China, Huazhong University of Science and Technology, Wuhan 430074, China J. Zheng · X. Wang (B) · Z. Zeng School of Artificial Intelligence and Automation and the Key Laboratory of Image Processing and Intelligent Control of Education Ministry of China, Huazhong University of Science and Technology, Wuhan 430074, China e-mail: [email protected] S. He School of Physics and Electronics, Central South University, Changsha 410083, Hunan, China
In addition, it is also found that the number of the initial offset boosting coexisting double-scroll attractors is closely related to the total number of scrolls and ultimately tends to infinity with increasing the total number of scrolls, meaning the emergence of extreme multistability. Then, the random performance of the initial offset boosting coexisting double-scroll attractors is tested by the NIST test suite. Moreover, an encryption scheme based on them is also proposed. The obtained results show that they have excellent randomness and are suitable for image encryption application. Finally, numerical simulation results are well demonstrated by circuit experiments, showing the feasibility of the designed memristive multi-double-scroll HNN model. Keywords Memristor · Initial offset boosting · Hopfield neural network (HNN) · Multi-double-scroll attractor · Amplitude control · Extreme multistability
1 Introduction Human brain is a highly complex nonlinear system, which consists of a large number of neurons. As we know, electrical activities between neurons usually exhibit complex chaotic dynamics [1–3]. The dynamics of brain signals exhibiting stochastic characteristics (chaotic behaviors) can be observed by electroencephalograms (EEGs) [4]. To further explore the mysteries
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