Design of an assemble-type fractional-order unit circuit and its application in Lorenz system

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 = 1 dB/2 dB/3 dB. 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.