CN103997400A - Method and circuit for different-fractional-order y<2>-containing Liu chaotic switching system - Google Patents
Method and circuit for different-fractional-order y<2>-containing Liu chaotic switching system Download PDFInfo
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- CN103997400A CN103997400A CN201410062473.4A CN201410062473A CN103997400A CN 103997400 A CN103997400 A CN 103997400A CN 201410062473 A CN201410062473 A CN 201410062473A CN 103997400 A CN103997400 A CN 103997400A
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- A fractional-order different containing y 2liu chaos switched system method, it is characterized in that being, comprise the following steps:(1) containing y 2the equation of Liu chaos system i be:(2) 0.9 rank are containing y 2the equation of Liu chaos system ii be:(3) 0.1 rank are containing y 2the equation of Liu chaos system iii be:(4) structure switching function q=f (x), wherein the expression formula iv of f (x) is:(5) by ii, iii and iv construct a kind of fractional-order different containing y 2liu chaos switched system v be:(6) according to fractional-order different containing y 2liu chaos switched system v constructing analog Circuits System, utilize operational amplifier U1, operational amplifier U2 and resistance and electric capacity form the fractional order inverting integrator of anti-phase adder and different orders, utilize multiplier U3 and multiplier U4 to realize multiplying, utilize analog switch U5 to realize the selection output of analog signal, described operational amplifier U1 and operational amplifier U2 adopt LF347D, described multiplier U3 and multiplier U4 adopt AD633JN, described analog switch U5 adopts ADG888, described operational amplifier U1 connects multiplier U3, multiplier U4 and analog switch U5, described operational amplifier U2 connects multiplier U3 and analog switch U5, described multiplier U3 concatenation operation amplifier U1, described multiplier U4 concatenation operation amplifier U2, described analog switch U5 concatenation operation amplifier U1 and operational amplifier U2,The 1st pin of described operational amplifier U1 joins by resistance R 3 and the 2nd pin of operational amplifier U1, join by resistance R 7 and the 6th pin of operational amplifier U1, the 3rd of operational amplifier U1, 5, 10, 12 pin ground connection, the 4th pin meets VCC, the 11st pin meets VEE, the 6th pin of operational amplifier U1 is in parallel by resistance R y11 and capacitor C y11's, connecting resistance Ry12 is in parallel with capacitor C y12's, again after connecting resistance Ry13 and capacitor C y13 in parallel, connect again the 7th pin of analog switch U5, in parallel by resistance R y21 and capacitor C y21, connecting resistance Ry22 is in parallel with capacitor C y22's, again after connecting resistance Ry23 and capacitor C y23 in parallel, connect again the 5th pin of analog switch U5, the 7th pin of operational amplifier U1 connects the 13rd pin of operational amplifier U1 by resistance R 2, meet the 1st of multiplier U4, 3 pins, the 8th pin of operational amplifier U1 connects the 2nd pin of operational amplifier U1 by resistance R 4, connect the 9th pin of operational amplifier U1 by resistance R 5, connect the 2nd pin of operational amplifier U2, connect the 1st pin of multiplier U3, the 9th pin of operational amplifier U1 is in parallel by resistance R x11 and capacitor C x11's, connecting resistance Rx12 is in parallel with capacitor C x12's, again after connecting resistance Rx13 and capacitor C x13 in parallel, connect again the 2nd pin of analog switch U5, in parallel by resistance R x21 and capacitor C x21, connecting resistance Rx22 is in parallel with capacitor C x22's, again after connecting resistance Rx23 and capacitor C x23 in parallel, connect again the 4th pin of analog switch U5, the 14th pin of operational amplifier U1 connects the 13rd pin of operational amplifier U1 by resistance R 1, connect the 9th pin of operational amplifier U1 by resistance R 6,The 6th of described operational amplifier U2, 7 pins are unsettled, the 3rd of described operational amplifier U2, 5, 10, 12 pin ground connection, the 4th pin meets VCC, the 11st pin meets VEE, the 1st pin of operational amplifier U2 is by the series connection ground connection of resistance R 13 and R14, meet the 8th of analog switch U5 by R13, 9 pins, the 8th pin of operational amplifier U2 connects the 9th pin of operational amplifier U2 by resistance R 11, connect the 3rd pin of multiplier U3, the 9th pin of operational amplifier U2 is in parallel by resistance R z11 and capacitor C z11's, connecting resistance Rz12 is in parallel with capacitor C z12's, again after connecting resistance Rz13 and capacitor C z13 in parallel, connect again the 10th pin of analog switch U5, in parallel by resistance R z21 and capacitor C z21, connecting resistance Rz22 is in parallel with capacitor C z22's, again after connecting resistance Rz23 and capacitor C z23 in parallel, connect again the 12nd pin of analog switch U5, the 14th pin of operational amplifier U2 connects the 13rd pin of operational amplifier U2 by resistance R 10, connect the 9th pin of operational amplifier U2 by resistance R 12,The 1st pin of described multiplier U3 connects the 8th pin of operational amplifier U1, the 3rd pin connects the 8th pin of operational amplifier U2, the equal ground connection of the 2nd, 4,6 pin, and the 5th pin meets VEE, the 7th pin connects the 6th pin of operational amplifier U1 by resistance R 8, the 8th pin meets VCC;The 1st, 3 pins of described multiplier U4 connect the 7th pin of operational amplifier U1, the equal ground connection of the 2nd, 4,6 pin, and the 5th pin meets VEE, and the 7th pin connects the 13rd pin of operational amplifier U2 by resistance R 9, and the 8th pin meets VCC;The 1st pin of described analog switch U5 meets VCC, the 16th pin ground connection, and the 13rd, 14,15 pins are unsettled, and the 3rd pin connects the 8th pin of operational amplifier U1, and the 6th pin connects the 7th pin of operational amplifier U1, and the 11st pin connects the 8th pin of operational amplifier U2.
- A fractional-order different containing y 2liu chaos switched system circuit, it is characterized in that being, utilize operational amplifier U1, operational amplifier U2 and resistance and electric capacity form the fractional order inverting integrator of anti-phase adder and different orders, utilize multiplier U3 and multiplier U4 to realize multiplying, utilize analog switch U5 to realize the selection output of analog signal, described operational amplifier U1 and operational amplifier U2 adopt LF347D, described multiplier U3 and multiplier U4 adopt AD633JN, described analog switch U5 adopts ADG888, described operational amplifier U1 connects multiplier U3, multiplier U4 and analog switch U5, described operational amplifier U2 connects multiplier U3 and analog switch U5, described multiplier U3 concatenation operation amplifier U1, described multiplier U4 concatenation operation amplifier U2, described analog switch U5 concatenation operation amplifier U1 and operational amplifier U2,The 1st pin of described operational amplifier U1 joins by resistance R 3 and the 2nd pin of operational amplifier U1, join by resistance R 7 and the 6th pin of operational amplifier U1, the 3rd of operational amplifier U1, 5, 10, 12 pin ground connection, the 4th pin meets VCC, the 11st pin meets VEE, the 6th pin of operational amplifier U1 is in parallel by resistance R y11 and capacitor C y11's, connecting resistance Ry12 is in parallel with capacitor C y12's, again after connecting resistance Ry13 and capacitor C y13 in parallel, connect again the 7th pin of analog switch U5, in parallel by resistance R y21 and capacitor C y21, connecting resistance Ry22 is in parallel with capacitor C y22's, again after connecting resistance Ry23 and capacitor C y23 in parallel, connect again the 5th pin of analog switch U5, the 7th pin of operational amplifier U1 connects the 13rd pin of operational amplifier U1 by resistance R 2, meet the 1st of multiplier U4, 3 pins, the 8th pin of operational amplifier U1 connects the 2nd pin of operational amplifier U1 by resistance R 4, connect the 9th pin of operational amplifier U1 by resistance R 5, connect the 2nd pin of operational amplifier U2, connect the 1st pin of multiplier U3, the 9th pin of operational amplifier U1 is in parallel by resistance R x11 and capacitor C x11's, connecting resistance Rx12 is in parallel with capacitor C x12's, again after connecting resistance Rx13 and capacitor C x13 in parallel, connect again the 2nd pin of analog switch U5, in parallel by resistance R x21 and capacitor C x21, connecting resistance Rx22 is in parallel with capacitor C x22's, again after connecting resistance Rx23 and capacitor C x23 in parallel, connect again the 4th pin of analog switch U5, the 14th pin of operational amplifier U1 connects the 13rd pin of operational amplifier U1 by resistance R 1, connect the 9th pin of operational amplifier U1 by resistance R 6,The 6th of described operational amplifier U2, 7 pins are unsettled, the 3rd of described operational amplifier U2, 5, 10, 12 pin ground connection, the 4th pin meets VCC, the 11st pin meets VEE, the 1st pin of operational amplifier U2 is by the series connection ground connection of resistance R 13 and R14, meet the 8th of analog switch U5 by R13, 9 pins, the 8th pin of operational amplifier U2 connects the 9th pin of operational amplifier U2 by resistance R 11, connect the 3rd pin of multiplier U3, the 9th pin of operational amplifier U2 is in parallel by resistance R z11 and capacitor C z11's, connecting resistance Rz12 is in parallel with capacitor C z12's, again after connecting resistance Rz13 and capacitor C z13 in parallel, connect again the 10th pin of analog switch U5, in parallel by resistance R z21 and capacitor C z21, connecting resistance Rz22 is in parallel with capacitor C z22's, again after connecting resistance Rz23 and capacitor C z23 in parallel, connect again the 12nd pin of analog switch U5, the 14th pin of operational amplifier U2 connects the 13rd pin of operational amplifier U2 by resistance R 10, connect the 9th pin of operational amplifier U2 by resistance R 12,The 1st pin of described multiplier U3 connects the 8th pin of operational amplifier U1, the 3rd pin connects the 8th pin of operational amplifier U2, the equal ground connection of the 2nd, 4,6 pin, and the 5th pin meets VEE, the 7th pin connects the 6th pin of operational amplifier U1 by resistance R 8, the 8th pin meets VCC;The 1st, 3 pins of described multiplier U4 connect the 7th pin of operational amplifier U1, the equal ground connection of the 2nd, 4,6 pin, and the 5th pin meets VEE, and the 7th pin connects the 13rd pin of operational amplifier U2 by resistance R 9, and the 8th pin meets VCC;The 1st pin of described analog switch U5 meets VCC, the 16th pin ground connection, and the 13rd, 14,15 pins are unsettled, and the 3rd pin connects the 8th pin of operational amplifier U1, and the 6th pin connects the 7th pin of operational amplifier U1, and the 11st pin connects the 8th pin of operational amplifier U2.
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Cited By (2)
Publication number | Priority date | Publication date | Assignee | Title |
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CN104468076A (en) * | 2014-11-11 | 2015-03-25 | 王晓红 | 0.8-order Liu chaotic system circuit realizing method based on chain type fractional order integral circuit module |
WO2016041104A1 (en) * | 2014-09-19 | 2016-03-24 | 李建庆 | 0.3-order lü chaotic system circuit based on chain fractional integrator circuit module |
Citations (3)
Publication number | Priority date | Publication date | Assignee | Title |
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US20100054225A1 (en) * | 2006-12-01 | 2010-03-04 | The European Gnss Supervisory Authority | Chaotic spreading codes and their generation |
CN102903282A (en) * | 2012-10-26 | 2013-01-30 | 玉林师范学院 | Integer-order and fractional-order multifunctional chaotic experiment instrument |
CN103152158A (en) * | 2013-01-30 | 2013-06-12 | 王少夫 | Three-dimensional chaotic system |
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US20100054225A1 (en) * | 2006-12-01 | 2010-03-04 | The European Gnss Supervisory Authority | Chaotic spreading codes and their generation |
CN102903282A (en) * | 2012-10-26 | 2013-01-30 | 玉林师范学院 | Integer-order and fractional-order multifunctional chaotic experiment instrument |
CN103152158A (en) * | 2013-01-30 | 2013-06-12 | 王少夫 | Three-dimensional chaotic system |
Cited By (2)
Publication number | Priority date | Publication date | Assignee | Title |
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WO2016041104A1 (en) * | 2014-09-19 | 2016-03-24 | 李建庆 | 0.3-order lü chaotic system circuit based on chain fractional integrator circuit module |
CN104468076A (en) * | 2014-11-11 | 2015-03-25 | 王晓红 | 0.8-order Liu chaotic system circuit realizing method based on chain type fractional order integral circuit module |
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