The Analysis of Symmetrical Behavior for a Dual Flux-controlled Memristive Shinriki Oscillator Based on FPGA

Fuhong MIN; Hongliang ZHENG; Zhi RUI; Yi CAO

doi:10.11999/JEIT201079

Volume 43 Issue 11

Nov. 2021

Turn off MathJax

Article Contents

Article Navigation > Journal of Electronics & Information Technology > 2021 > 43(11): 3384-3392

Fuhong MIN, Hongliang ZHENG, Zhi RUI, Yi CAO. The Analysis of Symmetrical Behavior for a Dual Flux-controlled Memristive Shinriki Oscillator Based on FPGA[J]. Journal of Electronics & Information Technology, 2021, 43(11): 3384-3392. doi: 10.11999/JEIT201079

Citation:

Fuhong MIN, Hongliang ZHENG, Zhi RUI, Yi CAO. The Analysis of Symmetrical Behavior for a Dual Flux-controlled Memristive Shinriki Oscillator Based on FPGA[J]. Journal of Electronics & Information Technology, 2021, 43(11): 3384-3392. doi: 10.11999/JEIT201079

Citation:

PDF( 13754 KB)

The Analysis of Symmetrical Behavior for a Dual Flux-controlled Memristive Shinriki Oscillator Based on FPGA

doi: 10.11999/JEIT201079

School of Electrical and Automation Engineering, Nanjing Normal University, Nanjing 210046, China

Funds: The National Natural Science Foundation of China (61971228)

Received Date: 2020-12-25
Rev Recd Date: 2021-05-25

Available Online: 2021-08-12

Publish Date: 2021-11-23

Abstract

Abstract

In this paper, a passive flux-controlled memristor is used to replace the diode series-parallel branch in the Shinriki oscillator, and the active flux-controlled memristor is introduced to substitute the resistance in the RLC resonant loop. At the same time, a series resistance is connected in the inductance branch to obtain a new type of dual flux-controlled memristive Shinriki oscillator. Through the coexisting bifurcation diagram of specific parameters and the Lyapunov exponential spectrum, the symmetric bifurcation behavior of oscillators is innovatively discovered, and the symmetry of the motion state distribution is shown in the two-parameter plane. Meanwhile, in the basin of attraction of the symmetrical parameter-initial value plane, the multistable characteristics of the system in the symmetrical domain are analyzed. The existence of symmetrical antimonotonic phenomena, the symmetrical coexistence of attractors with multiple motion states, and the incomplete symmetry behavior that depends on the initial value in the symmetric domain are studied. In addition, the digital circuit experiment of the dual flux-controlled memristive Shinriki oscillator is completed based on FPGA technology, and the waveform captured on the oscilloscope verifies the correctness of the system’s symmetrical dynamic behavior analysis.
- Dual flux-controlled memristive Shinriki oscillator,
- Symmetrical dynamic behaviors,
- Multistability,
- Antimonotonicity,
- Incompletely symmetrical behaviors

FullText(HTML)

References(20)

References

[1]	CHUA L. Memristor-the missing circuit element[J]. IEEE Transactions on Circuit Theory, 1971, 18(5): 507–519. doi: 10.1109/TCT.1971.1083337
[2]	CHEN Mo, SUN Mengxia, BAO Han, et al. Flux-charge analysis of two-memristor-based Chua’s circuit: Dimensionality decreasing model for detecting extreme multistability[J]. IEEE Transactions on Industrial Electronics, 2020, 67(3): 2197–2206. doi: 10.1109/TIE.2019.2907444
[3]	BAO Bocheng, HOU Liping, ZHU Yongxin, et al. Bifurcation analysis and circuit implementation for a tabu learning neuron model[J]. AEU-International Journal of Electronics and Communications, 2020, 121: 153235. doi: 10.1016/j.aeue.2020.153235
[4]	LI Shaolin, HE Yinghui, and CAO Hongjun. Necessary conditions for complete synchronization of a coupled chaotic aihara neuron network with electrical synapses[J]. International Journal of Bifurcation and Chaos, 2019, 29(5): 1950063. doi: 10.1142/S0218127419500639
[5]	李付鹏, 刘敬彪, 王光义, 等. 基于混沌集的图像加密算法[J]. 电子与信息学报, 2020, 42(4): 981–987. doi: 10.11999/JEIT190344 LI Fupeng, LIU Jingbiao, WANG Guangyi, et al. An image encryption algorithm based on chaos set[J]. Journal of Electronics &Information Technology, 2020, 42(4): 981–987. doi: 10.11999/JEIT190344
[6]	吴洁宁, 王丽丹, 段书凯. 基于忆阻器的时滞混沌系统及伪随机序列发生器[J]. 物理学报, 2017, 66(3): 030502. doi: 10.7498/aps.66.030502 WU Jiening, WANG Lidan, and DUAN Shukai. A memristor-based time-delay chaotic systems and pseudo-random sequence generator[J]. Acta Physica Sinica, 2017, 66(3): 030502. doi: 10.7498/aps.66.030502
[7]	曾以成, 成德武, 谭其威. 简洁无电感忆阻混沌电路及其特性[J]. 电子与信息学报, 2020, 42(4): 862–869. doi: 10.11999/JEIT190859 ZENG Yicheng, CHENG Dewu, and TAN Qiwei. A simple inductor-free memristive chaotic circuit and its characteristics[J]. Journal of Electronics &Information Technology, 2020, 42(4): 862–869. doi: 10.11999/JEIT190859
[8]	WANG Chunhua, XIA Hu, and ZHOU Ling. A memristive hyperchaotic multiscroll jerk system with controllable scroll numbers[J]. International Journal of Bifurcation and Chaos, 2017, 27(6): 1750091. doi: 10.1142/s0218127417500912
[9]	CHEN Mo, QI Jianwei, WU Huagan, et al. Bifurcation analyses and hardware experiments for bursting dynamics in non-autonomous memristive FitzHugh-Nagumo circuit[J]. Science China Technological Sciences, 2020, 63(6): 1035–1044. doi: 10.1007/s11431-019-1458-5
[10]	WU Huagan, BAO Bocheng, LIU Zhong, et al. Chaotic and periodic bursting phenomena in a memristive Wien-bridge oscillator[J]. Nonlinear Dynamics, 2016, 83(1): 893–903. doi: 10.1007/s11071-015-2375-8
[11]	WU Huagan, YE Yi, CHEN Mo, et al. Extremely slow passages in low-pass filter-based memristive oscillator[J]. Nonlinear Dynamics, 2019, 97(4): 2339–2353. doi: 10.1007/s11071-019-05131-1
[12]	HUA Mengjie, YANG Shuo, XU Quan, et al. Symmetrically scaled coexisting behaviors in two types of simple jerk circuits[J]. Circuit World, 2020, 47(1): 61–70. doi: 10.1108/CW-02-2020-0028
[13]	吕晏旻, 闵富红. 基于现场可编程逻辑门阵列的磁控忆阻电路对称动力学行为分析[J]. 物理学报, 2019, 68(13): 130502. doi: 10.7498/aps.68.20190453 LV Yanmin and MIN Fuhong. Dynamic analysis of symmetric behavior in flux-controlled memristor circuit based on field programmable gate array[J]. Acta Physica Sinica, 2019, 68(13): 130502. doi: 10.7498/aps.68.20190453
[14]	LI Chuang, MIN Fuhong, and LI Chunbiao. Multiple coexisting attractors of the serial–parallel memristor-based chaotic system and its adaptive generalized synchronization[J]. Nonlinear Dynamics, 2018, 94(4): 2785–2806. doi: 10.1007/s11071-018-4524-3
[15]	CHANG Hui, LI Yuxia, YUAN Fang, et al. Extreme multistability with hidden attractors in a simplest memristor-based circuit[J]. International Journal of Bifurcation and Chaos, 2019, 29(6): 1950086. doi: 10.1142/S021812741950086X
[16]	BAO Han, LIU Wenbo, and CHEN Mo. Hidden extreme multistability and dimensionality reduction analysis for an improved non-autonomous memristive FitzHugh–Nagumo circuit[J]. Nonlinear Dynamics, 2019, 96(3): 1879–1894. doi: 10.1007/s11071-019-04890-1
[17]	BAO Bocheng, XU Li, WANG Ning, et al. Third-order RLCM-four-elements-based chaotic circuit and its coexisting bubbles[J]. AEU-International Journal of Electronics and Communications, 2018, 94: 26–35. doi: 10.1016/j.aeue.2018.06.042
[18]	ZHANG Sen and ZENG Yicheng. A simple Jerk-like system without equilibrium: Asymmetric coexisting hidden attractors, bursting oscillation and double full Feigenbaum remerging trees[J]. Chaos, Solitons & Fractals, 2019, 120: 25–40. doi: 10.1016/j.chaos.2018.12.036
[19]	BAO Bocheng, HU Aihuang, BAO Han, et al. Three-dimensional memristive hindmarsh–rose neuron model with hidden coexisting asymmetric behaviors[J]. Complexity, 2018, 2018: 3872573. doi: 10.1155/2018/3872573
[20]	SHINRIKI M, YAMAMOTO M, and MORI S. Multimode oscillations in a modified Van Der Pol oscillator containing a positive nonlinear conductance[J]. Proceedings of the IEEE, 1981, 69(3): 394–395. doi: 10.1109/PROC.1981.11973