Four-wing hyperchaotic attractor generated from a new 4D system with one equilibrium and its fractional-order form

Nonlinear Dynamics

Volumn 67, Issue 2, 2012, Pages 1161-1173

  Dadras, Sara ^a   Momeni, Hamid Reza ^a   Qi, Guoyuan ^b   Wang, Zhong Lin ^c  

^a TARBIAT MODARES UNIVERSITY   (Iran)

^b TSHWANE UNIVERSITY OF TECHNOLOGY   (South Africa)

^c BINZHOU UNIVERSITY   (China)

Author keywords

Four wing hyperchaotic attractor; Fractional order system; Lyapunov exponent; Poincar mapping

Indexed keywords

ANALYSIS APPROACH; AUTONOMOUS SYSTEMS; BIFURCATION DIAGRAM; CHAOTIC ATTRACTORS; DYNAMICAL BEHAVIORS; EQUILIBRIUM POINT; FRACTIONAL-ORDER SYSTEMS; HYPERCHAOTIC; LYAPUNOV EXPONENT; PHASE PORTRAIT; POINCARE;

DIFFERENTIAL EQUATIONS; DYNAMIC ANALYSIS; LYAPUNOV FUNCTIONS; LYAPUNOV METHODS; TIME SERIES; TIME SERIES ANALYSIS;

CHAOTIC SYSTEMS;

EID: 84855761900     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-011-0060-0     Document Type: Article

References (57)

1. E.N. Lorenz 1963 Deterministic nonperiodic flow J. Atmos. Sci. 20 130 141 10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2
2. J. Chakravorty T. Banerjee R. Ghatak A. Bose B.C. Sarkar 2009 Generating chaos in injection-synchronized Gunn oscillator: an experimental approach IETE J. Res. 55 106 111 10.4103/0377-2063.54894
3. B. Nana P. Woafo S. Domngang 2009 Chaotic synchronization with experimental application to secure communication Commun. Nonlinear Sci. Numer. Simul. 14 629 655
4. M. Coulon D. Roviras 2009 Multi-user receivers for synchronous and asynchronous transmission for chaos-based multiple-access systems Signal Process. 89 583 598 10.1016/j.sigpro.2008.10.015 1157.94326
5. S. Kozic M. Hasler 2009 Low-density codes based on chaotic systems for simple encoding IEEE Trans. Circuits Syst. I 56 405 415 10.1109/TCSI.2008. 2008433
6. G. Chen T. Ueta 1999 Yet another chaotic attractor Int. J. Bifurc. Chaos 9 1465 1466 10.1142/S0218127499001024 0962.37013 1729683 (Pubitemid 129292251)
7. J. Lü G. Chen 2002 A new chaotic attractor coined Int. J. Bifurc. Chaos 12 659 661 10.1142/S0218127402004620 1063.34510 (Pubitemid 34862041)
8. G. Qi G. Chen S. Du Z. Chen Z. Yuan 2005 Analysis of a new chaotic system Physica A 352 295 308 10.1016/j.physa.2004.12.040 (Pubitemid 40612606)
9. G.Y. Wang S.S. Qui H.W. Li C.F. Li Y. Zheng 2006 A new chaotic system and its circuit realization Chin. Phys. 15 2872 2877 10.1088/1009-1963/15/12/018 (Pubitemid 46070072)
10. C. Liu L. Liu 2008 A new three-dimensional autonomous chaotic oscillation system J. Phys. Conf. Ser. 96 012173 10.1088/1742-6596/96/1/012173
11. Z. Chen Y. Yang Z. Yuan 2008 A single three-wing or four-wing chaotic attractor generated from a three-dimensional smooth quadratic autonomous system Chaos Solitons Fractals 38 1187 1196 10.1016/j.chaos.2007.01.058 1152.37312 2435612
12. L. Wang 2009 3-scroll and 4-scroll chaotic attractors generated from a new 3-D quadratic autonomous system Nonlinear Dyn. 56 453 462 10.1007/s11071-008-9417-4 1204.70021
13. S. Dadras H.R. Momeni 2009 A novel three-dimensional autonomous chaotic system generating two-, three- and four-scroll attractors Phys. Lett. A 373 3637 3642 10.1016/j.physleta.2009.07.088 2571878
14. E. Baghious P. Jarry 1993 Lorenz attractor: From differential equations with piecewise-linear terms Int. J. Bifurc. Chaos 3 201 210 10.1142/ S0218127493000155 0873.34045 1218724
15. A. Elwakil S. Ozoguz M. Kennedy 2002 Creation of a complex butterfly attractor using a novel Lorenz-type system IEEE Trans. Circuits Syst. I 49 527 530 10.1109/81.995671 1911024 (Pubitemid 34515157)
16. S. Ozoguz A. Elwakil M. Kennedy 2002 Experimental verification of the butterfly attractor in a modified Lorenz system Int. J. Bifurc. Chaos 12 1627 1632 10.1142/S0218127402005364
17. G. Qi G. Chen S. Li Y. Zhang 2006 Four-wing attractors: From pseudo to real Int. J. Bifurc. Chaos 16 859 885 10.1142/S0218127406015180 1111.37025 2234260 (Pubitemid 43936687)
18. G. Grassi F.L. Severance E.D. Mashev B.J. Bazuin D.A. Miller 2008 Generation of a four-wing chaotic attractor by two weakly-coupled Lorenz systems Int. J. Bifurc. Chaos 18 2089 2094 10.1142/S0218127408021580 1156.37006
19. G. Grassi 2008 Novel four-wing and eight-wing attractors using coupled chaotic Lorenz systems Chin. Phys. B 17 3247 3251 10.1088/1674-1056/17/9/017
20. S. Dadras H.R. Momeni G. Qi 2010 Analysis of a new 3D smooth autonomous system with different wing chaotic attractors and transient chaos Nonlinear Dyn. 62 391 405 10.1007/s11071-010-9726-2 05841014 2737002
21. L. Wang 2009 Yet another 3D quadratic autonomous system generating three-wing and four-wing chaotic attractors Chaos 19 013107 10.1063/1.3070648 2513755
22. S. Dadras H.R. Momeni 2010 Generating one-, two-, three- and four-scroll attractors from a novel four-dimensional smooth autonomous chaotic system Chin. Phys. B 19 060506 10.1088/1674-1056/19/6/060506
23. O.E. Rössler 1979 An equation for hyperchaos Phys. Lett. A 71 155 157 10.1016/0375-9601(79)90150-6 0996.37502 588951
24. K. Thamilmaran M. Lakshmanan A. Venkatesan 2004 Hyperchaos in a modified canonical Chua's circuit Int. J. Bifurc. Chaos 14 221 243 10.1142/ S0218127404009119 1067.94597 (Pubitemid 39501653)
25. Y. Li S.K. Tang G. Chen 2005 Generating hyperchaos via state feedback control Int. J. Bifurc. Chaos 15 3367 3375 10.1142/S0218127405013988 (Pubitemid 41831956)
26. Y. Li W.K.S. Tang G. Chen 2005 Hyperchaos evolved from the generalized Lorenz equation Int. J. Circuit Theory Appl. 33 235 251 10.1002/cta.318 1079.34032 (Pubitemid 41068374)
27. J.Z. Wang Z.Q. Chen Z.Z. Yuan 2006 The generation of a hyperchaotic system based on a three-dimensional autonomous chaotic system Chin. Phys. 15 1216 1225 10.1088/1009-1963/15/6/015 (Pubitemid 44149728)
28. Q. Jia 2007 Generation and suppression of a new hyperchaotic system with double hyperchaotic attractors Phys. Lett. A 371 410 415 10.1016/j.physleta. 2007.06.038 1209.37033 2412425
29. Q. Jia 2007 Hyperchaos generated from the Lorenz chaotic system and its control Phys. Lett. A 366 217 222 10.1016/j.physleta.2007.02.024 1203.93086
30. G. Qi M.A. Wyk B.J. Wyk G. Chen 2008 On a new hyperchaotic system Phys. Lett. A 372 124 136 10.1016/j.physleta.2007.10.082 1217.37032 2374285
31. L. Liu C. Liu Y. Zhang 2008 Analysis of a novel four-dimensional hyperchaotic system Chin. J. Phys. 46 386 393
32. W.J. Wu Z.Q. Chan Z.Z. Yuan 2008 Local bifurcation analysis of a four-dimensional hyperchaotic system Chin. Phys. B 17 2420 2432 10.1088/1674-1056/17/7/015
33. G.M. Mahmoud M.A. Al-Kashif A.A. Farghaly 2008 Chaotic and hyperchaotic attractors of a complex nonlinear system J. Phys. A, Math. Theor. 41 055104 10.1088/1751-8113/41/5/055104 2433424
34. N. Yujun W. Xingyuan W. Mingjun Z. Huaguang 2010 A new hyperchaotic system and its circuit implementation Commun. Nonlinear Sci. Numer. Simul. 15 3518 3524 10.1016/j.cnsns.2009.12.005
35. S. Zheng G. Dong Q. Bi 2010 A new hyperchaotic system and its synchronization Appl. Math. Comput. 215 3192 3200 10.1016/j.amc.2009.09.060 1188.34051 2576807
36. G.M. Mahmoud E.E. Mahmoud M.E. Ahmed 2009 On the hyperchaotic complex Lü system Nonlinear Dyn. 58 725 738 10.1007/s11071-009-9513-0 1183.70053 2563618
37. G. Qi M.A. Wyk B.J. Wyk G. Chen 2009 A new hyperchaotic system and its circuit implementation Chaos Solitons Fractals 40 2544 2549 10.1016/j.chaos. 2007.10.053
38. Q. Yang K. Zhang G. Chen 2009 Hyperchaotic attractors from a linearly controlled Lorenz system Nonlinear Anal.; Real World Appl. 10 1601 1617 10.1016/j.nonrwa.2008.02.008 1175.37041 2502969
39. C.H. Chen L.J. Sheu H.K. Chen J.H. Chen H.C. Wang Y.C. Chao Y.K. Lin 2009 A new hyper-chaotic system and its synchronization Nonlinear Anal.; Real World Appl. 10 2088 2096 10.1016/j.nonrwa.2008.03.015 1163.65337 2508418
40. Z. Chen Y. Yang G. Qi Z. Yuan 2007 A novel hyperchaos system only with one equilibrium Phys. Lett. A 360 696 701 10.1016/j.physleta.2006.08.085 2287760 (Pubitemid 44791796)
41. C. Liu 2007 A new hyperchaotic dynamical system Chin. Phys. 16 3279 3284 10.1088/1009-1963/16/11/022 (Pubitemid 350176532)
42. S. Cang G. Qi Z. Chen 2010 A four-wing hyper-chaotic attractor and transient chaos generated from a new 4-D quadratic autonomous system Nonlinear Dyn. 59 515 527 10.1007/s11071-009-9558-0 1183.70049 2592934
43. G. Grassi F.L. Severance D.A. Miller 2009 Multi-wing hyperchaotic attractors from coupled Lorenz systems Chaos Solitons Fractals 41 284 291 10.1016/j.chaos.2007.12.003 1198.37045
44. N. Makris M.C. Constantinou 1991 Fractional derivative Maxwell model for viscous dampers J. Struct. Eng. 117 2708 2724 10.1061/(ASCE)0733-9445(1991)117: 9(2708) (Pubitemid 21697432)
45. E. Scalas R. Gorenflo F. Mainardi 2000 Fractional calculus and continuous-time finance Physica A 284 376 384 10.1016/S0378-4371(00)00255-7 1773804
46. Cafagna, D.: Fractional calculus: a mathematical tool from the past for present engineers. IEEE Ind. Electron. Mag. (summer), 35-40 (2007) (Pubitemid 350141726)
47. M.S. Tavazoei M. Haeri S. Bolouki M. Siami 2009 Using fractional-order integrator to control chaos in single-input chaotic system Nonlinear Dyn. 55 179 190 10.1007/s11071-008-9353-3 1220.70025 2466113
48. D. Cafagna G. Grassi 2008 Bifurcation and chaos in the fractional-order Chen system via a time-domain approach Int. J. Bifurc. Chaos 18 1845 1863 10.1142/S0218127408021415 1158.34300 2454066
49. D. Cafagna G. Grassi 2008 Fractional-order Chua's circuit: time domain analysis, bifurcation, chaotic behavior and test for chaos Int. J. Bifurc. Chaos 18 615 639 10.1142/S0218127408020550 1147.34302 2415859 (Pubitemid 351828395)
50. V. Daftardar-Gejji S. Bhalekar 2010 Chaos in fractional ordered Liu system Comput. Math. Appl. 59 1117 1127 10.1016/j.camwa.2009.08.018 1189.34081 2579477
51. D. Cafagna G. Grassi 2009 Fractional-order chaos: a novel four-wing attractor in coupled Lorenz systems Int. J. Bifurc. Chaos 19 3329 3338 10.1142/S0218127409024785 1182.34003
52. D. Cafagna G. Grassi 2009 Hyperchaos in the fractional-order Rössler system with lowest order Int. J. Bifurc. Chaos 19 339 347 10.1142/ S0218127409022890 1170.34327
53. K. Diethelm 1997 An algorithm for the numerical solution of differential equations of fractional order Electron. Trans. Numer. Anal. 5 1 6 0890.65071 1447831 (Pubitemid 38870919)
54. K. Diethelm N.J. Ford A.D. Freed 2002 A predictor-corrector approach for the numerical solution for fractional differential equations Nonlinear Dyn. 29 3 22 10.1023/A:1016592219341 1009.65049 1926466 (Pubitemid 34945390)
55. K. Diethelm N.J. Ford 2002 Analysis of fractional differential equations J. Math. Anal. Appl. 265 229 248 10.1006/jmaa.2000.7194 1014.34003 1876137
56. A. Charef H.H. Sun Y.Y. Tsao B. Onaral 1992 Fractal systems as represented by singularity function IEEE Trans. Autom. Control 37 1465 1470 10.1109/9.159595 0825.58027 1183117 (Pubitemid 23555835)
57. M.S. Tavazoei M. Haeri 2008 Limitation of frequency domain approximation for detecting chaos in fractional-order system Nonlinear Anal. Theory Methods Appl. 69 1299 1320 10.1016/j.na.2007.06.030 1148.65094 2426692