Journal
IET CIRCUITS DEVICES & SYSTEMS
Volume 11, Issue 5, Pages 437-445Publisher
INST ENGINEERING TECHNOLOGY-IET
DOI: 10.1049/iet-cds.2016.0145
Keywords
circuit simulation; chaos; nonlinear network analysis; circuit stability; transfer functions; Laplace equations; network synthesis; assemble-type fractional-order unit circuit design; generalised Lorenz three-dimensional integer-order nonlinear system; transfer functions; Laplace domain; chain type circuits; tree type circuits; mixed type circuits; new type circuits; circuit theory; circuit simulation; chaotic behaviours; stability analytical method; stability theorems; necessary conditions
Categories
Funding
- National Natural Science Foundation of China [61363076]
- Scientific Research Plan Projects of Jiangxi Education Department [GJJ14439, GJJ150621]
- Innovation Fund for Graduate Students in Jiangxi Province [YC2015-S290]
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A new generalised Lorenz three-dimensional integer-order non-linear system is constructed, and integer-order derivatives are simply replaced by fractional-order ones. Transfer functions in Laplace domain have been calculated and compared for a set of fractional orders q(i) in (0, 1) with decrement of 0.025 for the maximum error Y=1dB/2dB/3dB. A novel basic fractional-order unit circuit named 'Assemble Type' is designed consulting to the four existing unit circuits, which are 'Chain Type', 'Tree Type', 'Mixed Type' and 'New Type'. Meanwhile, it is compared with the four existing unit circuits in circuit theory and applications. The novel fractional-order unit circuit is applied to the circuit simulation of Lorenz system combined with the other four unit circuits, and circuit simulation shows that they have very resemble chaotic behaviours, actually, the scheme can be applied in any tiny values of q(i), which shows that the fractional-order system has better effectiveness, flexibility and universality. Finally, using stability analytical method based on two stability theorems and necessary conditions to exhibit validity and feasibility of this novel-type design.
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