Journal
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
Volume 20, Issue 1, Pages 29-41Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218127410025387
Keywords
Multi-wing butterfly attractor; Lorenz-type system; sawtooth wave function; circuit implementation
Funding
- National Natural Science Foundation of China [60772158, 60821091, 60871025, 60572073]
- Important Direction Project of Knowledge Innovation Program of Chinese Academy of Sciences [KJCX3-SYW-S01]
- National Basic Research (973) Program of China [2007CB310805]
- Natural Science Foundation of Guangdong Province [8151009001000060]
- Natural Science Foundation of Guangdong Province on Innovation Research Group [8351009001000002]
- Science and Technology Plan Project of Guangdong Province [2009B010800037]
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Lorenz system, as the first classical chaotic system, has been intensively investigated over the last four decades. Based on the sawtooth wave function, this paper initiates a novel approach for generating multi-wing butterfly chaotic attractors from the generalized first and second kinds of Lorenz-type systems. Compared with the traditional ring-shaped multi-scroll Lorenz chaotic attractors, the proposed multi-wing butterfly chaotic attractors are much easier to be designed and implemented by analog circuits. The dynamical behaviors of these multi-wing butterfly chaotic systems are further studied. Theoretical analysis shows that every index-2 saddle-focus equilibrium corresponds to a unique wing in the butterfly attractors. Finally, a module-based unified circuit diagram is constructed for realizing various multi-wing butterfly attractors. It should be especially pointed out that this is the first time in the literature that a maximal 10-wing butterfly chaotic attractor is experimentally verified by analog circuits.
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