Abstract
Based on the integer-order memristive system that can generate two-scroll, three-scroll, and four-scroll chaotic attractors, in this paper, we found other phenomena that two kinds of three-scroll chaotic attractors coexist in this system with different initial conditions. Furthermore, we proposed a coexisting fractional-order system based on the three-scroll chaotic attractors system, in which the three-scroll or four-scroll chaotic attractors emerged with different fractional-orders q. Meanwhile, with fractional-order q=0.965 and different initial conditions, coexistence of two kinds of three-scroll and four-scroll chaotic attractors is found simultaneously. Finally, we discussed controlling chaos for the fractional-order memristive chaotic system.
Highlights
We proposed a coexisting fractional-order system based on the three-scroll chaotic attractors system, in which the three-scroll or four-scroll chaotic attractors emerged with di erent fractional-orders
A fractional-order memristor-based simplest chaotic circuit with double-scroll and four-scroll attractors using fourth-degree polynomial [21] was reported by Teng et al and a fractional-order memristor-based chaotic system with single-scroll attractor and a stable equilibrium point [28] was reported by Prakash et al, and a fractional-order memristor-based chaotic system with coexisting attractors [1] was reported by Zhou and Ke
Some new results for the integer-order memristive system [1] are found. e coexistence of two kinds of three-scroll chaotic tractors emerges in the integer-order memristive system (1) with di erent initial conditions, which Zhou and Ke have not reported in reference [1]
Summary
Based on the integer-order memristive system that can generate two-scroll, three-scroll, and four-scroll chaotic attractors, in this paper, we found other phenomena that two kinds of three-scroll chaotic attractors coexist in this system with di erent initial conditions. We proposed a coexisting fractional-order system based on the three-scroll chaotic attractors system, in which the three-scroll or four-scroll chaotic attractors emerged with di erent fractional-orders. With fractionalorder = 0.965 and di erent initial conditions, coexistence of two kinds of three-scroll and four-scroll chaotic attractors is found simultaneously. We discussed controlling chaos for the fractional-order memristive chaotic system
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