Fractional-order memcapacitor-based Chua's circuit and its chaotic behaviour analysis

In this paper, a simulation model of the charge-controlled memcapacitor is realized, and fractional calculus is used to analyze it. An interesting phenomena found out is that the curve is bent downward as the parameter order-α decreases. And then, the fractional-order memcapacitor Chua's differential equations are presented. Theory analysis and simulation results show the influence of the fractional-order to the system dynamics. The nonlinear dynamics of the above fractional-order nonlinear system including phase graphs, time domain waveforms and bifurcation diagrams are studied in detail, during which many interesting phenomena are discovered. We observe that chaos seems to disappear as the order q decreases. Meanwhile, when q₁ =3D q₂ =3D q₃ =3D 0.90, the chaos disappeared completely. Finally, corresponding bifurcation diagram of variable Y versus parameter q, q₁, q₂ and q₃ are presented respectively, and get a conclusion that the order q₃ has the greatest influence on Chaos than q₁ and q₂.