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Theoretical analysis and experimental verification of fractional-order RC cobweb circuit network

Author

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  • Liu, Yang
  • Chen, Liping
  • Wu, Xiaobo
  • Lopes, António M.
  • Cui, Fengqi
  • Chen, YangQuan

Abstract

Recent research has shown that ideal capacitors and inductors do not physically exist, and that the dynamics of real devices can be accurately described by fractional-order (FO) mathematical models. This paper investigates a class of 2×n order RC cobweb FO circuit network with central node. Based on the Kirchhoff’s laws, the impedance magnitude and phase between two points of the network are derived using difference equations and matrix transformations. Three impedance expressions are deduced, and their correctness is verified numerically and by simulations. The influence of various parameters of the electrical network, namely the resistance, capacitance, number of circuit units, frequency and fractional order, on the impedance is studied. Additionally, for the first time, physical experiments are presented to compare the effectiveness of FO and integer-order circuit networks for describing the impedance of actual physical circuits. These experiments confirm that FO circuit network models perform better than the integer-order ones for representing the characteristics of the impedance magnitude and phase.

Suggested Citation

  • Liu, Yang & Chen, Liping & Wu, Xiaobo & Lopes, António M. & Cui, Fengqi & Chen, YangQuan, 2023. "Theoretical analysis and experimental verification of fractional-order RC cobweb circuit network," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    • Handle: RePEc:eee:chsofr:v:172:y:2023:i:c:s0960077923004423
    DOI: 10.1016/j.chaos.2023.113541
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    1. Chu, Yu-Ming & Bekiros, Stelios & Zambrano-Serrano, Ernesto & Orozco-López, Onofre & Lahmiri, Salim & Jahanshahi, Hadi & Aly, Ayman A., 2021. "Artificial macro-economics: A chaotic discrete-time fractional-order laboratory model," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    2. F. Merrikh Bayat & M. Prezioso & B. Chakrabarti & H. Nili & I. Kataeva & D. Strukov, 2018. "Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits," Nature Communications, Nature, vol. 9(1), pages 1-7, December.
    3. Amir Bashan & Ronny P. Bartsch & Jan. W. Kantelhardt & Shlomo Havlin & Plamen Ch. Ivanov, 2012. "Network physiology reveals relations between network topology and physiological function," Nature Communications, Nature, vol. 3(1), pages 1-9, January.
    4. Ahmad, Shabir & Ullah, Aman & Al-Mdallal, Qasem M. & Khan, Hasib & Shah, Kamal & Khan, Aziz, 2020. "Fractional order mathematical modeling of COVID-19 transmission," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
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