메뉴 건너뛰기




Volumn 69, Issue 3, 2012, Pages 805-816

Generating tri-chaos attractors with three positive Lyapunov exponents in new four order system via linear coupling

Author keywords

3 D parametric diagram; Lyapunov exponent; Mathieu van der Pol system; Tri Chaos

Indexed keywords

2-D AND 3-D PARAMETERS; 3-D PARAMETRIC DIAGRAM; ADVANCED APPLICATIONS; AUTONOMOUS SYSTEMS; COUPLED NONLINEAR SYSTEMS; FOUR-ORDER; HYPER-CHAOTIC SYSTEMS; HYPERCHAOTIC; LINEAR COUPLING; LYAPUNOV EXPONENT; MATHIEU-VAN DER POL SYSTEM; PHASE PORTRAIT; SECURE COMMUNICATIONS; TRI-CHAOS; VAN DER POL SYSTEMS;

EID: 84863988575     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-011-0306-x     Document Type: Article
Times cited : (22)

References (49)
  • 1
    • 80051786461 scopus 로고    scopus 로고
    • Chaotic ant swarm for the traveling salesman problem
    • Wei, Z., Ge, F., Lu, Y., Li, L., Yang, Y.: Chaotic ant swarm for the traveling salesman problem. Nonlinear Dyn. 65, 271-281 (2011)
    • (2011) Nonlinear Dyn. , vol.65 , pp. 271-281
    • Wei, Z.1    Ge, F.2    Lu, Y.3    Li, L.4    Yang, Y.5
  • 2
    • 82255181190 scopus 로고    scopus 로고
    • Analysis of a new threedimensional chaotic system
    • Zhang, X., Zhu, H., Yao, H.: Analysis of a new threedimensional chaotic system. Nonlinear Dyn. 67, 335-343 (2012)
    • (2012) Nonlinear Dyn. , vol.67 , pp. 335-343
    • Zhang, X.1    Zhu, H.2    Yao, H.3
  • 3
    • 74249108466 scopus 로고    scopus 로고
    • A novel study of parity and attractor in the time reversed Lorentz system
    • Li, S.Y., Ge, Z.M.: A novel study of parity and attractor in the time reversed Lorentz system. Phys. Lett. A 373, 4053-4059 (2009)
    • (2009) Phys. Lett. A , vol.373 , pp. 4053-4059
    • Li, S.Y.1    Ge, Z.M.2
  • 4
    • 77955654608 scopus 로고    scopus 로고
    • Nonlinear observer-based impulsive synchronization in chaotic systems with multiple attractors
    • Ghosh, D., Chowdhury, A.R.: Nonlinear observer-based impulsive synchronization in chaotic systems with multiple attractors. Nonlinear Dyn. 60, 607-613 (2010)
    • (2010) Nonlinear Dyn. , vol.60 , pp. 607-613
    • Ghosh, D.1    Chowdhury, A.R.2
  • 5
    • 79955368183 scopus 로고    scopus 로고
    • Fuzzy modeling and synchronization of chaotic quantum cellular neural networks nano system via a novel fuzzy model and its implementation on electronic circuits
    • Ge, Z.M., Li, S.Y.: Fuzzy modeling and synchronization of chaotic quantum cellular neural networks nano system via a novel fuzzy model and its implementation on electronic circuits. J. Comput. Theor. Nanosci. 7, 1-10 (2010)
    • (2010) J. Comput. Theor. Nanosci. , vol.7 , pp. 1-10
    • Ge, Z.M.1    Li, S.Y.2
  • 6
    • 84862845680 scopus 로고    scopus 로고
    • Absolute term introduced to rebuild the chaotic attractor with constant Lyapunov exponent spectrum
    • doi:10.1007/s11071-011-0239-4
    • Li, C., Wang, J., Hu, W.: Absolute term introduced to rebuild the chaotic attractor with constant Lyapunov exponent spectrum. Nonlinear Dyn. (2012). doi:10.1007/s11071-011-0239-4
    • (2012) Nonlinear Dyn.
    • Li, C.1    Wang, J.2    Hu, W.3
  • 7
    • 80051801979 scopus 로고    scopus 로고
    • Dynamical properties and simulation of a new Lorenz-like chaotic system
    • Li, X., Ou, Q.: Dynamical properties and simulation of a new Lorenz-like chaotic system. Nonlinear Dyn. 65, 255-270 (2011)
    • (2011) Nonlinear Dyn. , vol.65 , pp. 255-270
    • Li, X.1    Ou, Q.2
  • 8
    • 79959524471 scopus 로고    scopus 로고
    • Topological horseshoe analysis and the circuit implementation for a four-wing chaotic attractor
    • Jia, H.Y., Chen, Z.Q., Qi, G.Y.: Topological horseshoe analysis and the circuit implementation for a four-wing chaotic attractor. Nonlinear Dyn. 65, 131-140 (2011)
    • (2011) Nonlinear Dyn. , vol.65 , pp. 131-140
    • Jia, H.Y.1    Chen, Z.Q.2    Qi, G.Y.3
  • 9
    • 79959528048 scopus 로고    scopus 로고
    • A speech encryption using fractional chaotic systems
    • Sheu, L.J.: A speech encryption using fractional chaotic systems. Nonlinear Dyn. 65, 103-108 (2011)
    • (2011) Nonlinear Dyn. , vol.65 , pp. 103-108
    • Sheu, L.J.1
  • 10
    • 77954349450 scopus 로고    scopus 로고
    • Parameter identification of chaotic systems using improved differential evolution algorithm
    • Ho, W.H., Chou, J.H., Guo, C.Y.: Parameter identification of chaotic systems using improved differential evolution algorithm. Nonlinear Dyn. 61, 29-41 (2010)
    • (2010) Nonlinear Dyn. , vol.61 , pp. 29-41
    • Ho, W.H.1    Chou, J.H.2    Guo, C.Y.3
  • 12
    • 77949274584 scopus 로고    scopus 로고
    • A four-wing hyper-chaotic attractor and transient chaos generated from a new 4-D quadratic autonomous system
    • Cang, S., Qi, G., Chen, Z.: A four-wing hyper-chaotic attractor and transient chaos generated from a new 4-D quadratic autonomous system. Nonlinear Dyn. 59, 515-527 (2010)
    • (2010) Nonlinear Dyn. , vol.59 , pp. 515-527
    • Cang, S.1    Qi, G.2    Chen, Z.3
  • 13
    • 79955823797 scopus 로고    scopus 로고
    • A robust method on estimation of Lyapunov exponents from a noisy time series
    • Yang, C.,Wu, C.Q.: A robust method on estimation of Lyapunov exponents from a noisy time series. Nonlinear Dyn. 64, 279-292 (2011)
    • (2011) Nonlinear Dyn. , vol.64 , pp. 279-292
    • Yang, C.1    Wu, C.Q.2
  • 14
    • 0029275629 scopus 로고
    • A study of the chaotic behaviour of the elastic-plastic Euler arch
    • Bontempi, F.: A study of the chaotic behaviour of the elastic-plastic Euler arch. Nonlinear Dyn. 7, 217-229 (1995)
    • (1995) Nonlinear Dyn. , vol.7 , pp. 217-229
    • Bontempi, F.1
  • 15
    • 77949422942 scopus 로고    scopus 로고
    • On stability analysis via Lyapunov exponents calculated from a time series using nonlinear mapping-A case study
    • Yang, C., Wu, Q.: On stability analysis via Lyapunov exponents calculated from a time series using nonlinear mapping-A case study. Nonlinear Dyn. 59, 239-257 (2010)
    • (2010) Nonlinear Dyn. , vol.59 , pp. 239-257
    • Yang, C.1    Wu, Q.2
  • 16
    • 0037251324 scopus 로고    scopus 로고
    • Chaos, chaos control and synchronization of electro-mechanical gyrostat system
    • Ge, Z.M., Lin, T.N.: Chaos, chaos control and synchronization of electro-mechanical gyrostat system. Chaos Solitons Fractals 259, 585-603 (2003)
    • (2003) Chaos Solitons Fractals , vol.259 , pp. 585-603
    • Ge, Z.M.1    Lin, T.N.2
  • 17
    • 78049530750 scopus 로고    scopus 로고
    • The effects of fractional order on a 3-D quadratic autonomous system with four-wing attractor
    • Wang, Z., Sun, Y., Qi, G., Wyk, B.J.: The effects of fractional order on a 3-D quadratic autonomous system with four-wing attractor. Nonlinear Dyn. 62, 139-150 (2010)
    • (2010) Nonlinear Dyn. , vol.62 , pp. 139-150
    • Wang, Z.1    Sun, Y.2    Qi, G.3    Wyk, B.J.4
  • 18
    • 0942277650 scopus 로고    scopus 로고
    • Synchronization of unidirectional coupled chaotic systems via partial stability
    • Ge, Z.M., Chen, Y.S.: Synchronization of unidirectional coupled chaotic systems via partial stability. Chaos Solitons Fractals 21, 101-111 (2004)
    • (2004) Chaos Solitons Fractals , vol.21 , pp. 101-111
    • Ge, Z.M.1    Chen, Y.S.2
  • 19
    • 77954349412 scopus 로고    scopus 로고
    • Projective synchronization of new hyperchaotic system with fully unknown parameters
    • Ghosh, D., Bhattacharya, S.: Projective synchronization of new hyperchaotic system with fully unknown parameters. Nonlinear Dyn. 61, 11-12 (2010)
    • (2010) Nonlinear Dyn. , vol.61 , pp. 11-12
    • Ghosh, D.1    Bhattacharya, S.2
  • 21
    • 77955655688 scopus 로고    scopus 로고
    • Hopf bifurcation and intermittent transition to hyperchaos in a novel strong four-dimensional hyperchaotic system
    • Wu, W., Chen, Z.: Hopf bifurcation and intermittent transition to hyperchaos in a novel strong four-dimensional hyperchaotic system. Nonlinear Dyn. 60, 615-630 (2010)
    • (2010) Nonlinear Dyn. , vol.60 , pp. 615-630
    • Wu, W.1    Chen, Z.2
  • 22
    • 84858863293 scopus 로고    scopus 로고
    • A novel bounded 4D chaotic system
    • doi:10.1007/s11071-011-0159-3
    • Zhang, J., Tang, W.: A novel bounded 4D chaotic system. Nonlinear Dyn. (2012). doi:10.1007/s11071-011-0159-3
    • (2012) Nonlinear Dyn.
    • Zhang, J.1    Tang, W.2
  • 23
    • 78049462884 scopus 로고    scopus 로고
    • Two-level chaos-based video cryptosystem on H.263 codec
    • Chen, Z., Ip, W.H., Chan, C.Y., Yung, K.L.: Two-level chaos-based video cryptosystem on H.263 codec. Nonlinear Dyn. 62, 647-664 (2010)
    • (2010) Nonlinear Dyn. , vol.62 , pp. 647-664
    • Chen, Z.1    Ip, W.H.2    Chan, C.Y.3    Yung, K.L.4
  • 24
    • 0000263749 scopus 로고
    • Transition to hyperchaos in chaotically forced coupled oscillators
    • Kapitaniak, T.: Transition to hyperchaos in chaotically forced coupled oscillators. Phys. Rev. E 47, R2978 (1993)
    • (1993) Phys. Rev. E , vol.47
    • Kapitaniak, T.1
  • 25
    • 0030149488 scopus 로고    scopus 로고
    • Simple RC chaotic oscillator
    • Namajunas, A., Tamasevicius, A.: Simple RC chaotic oscillator. Electron. Lett. 32, 945-946 (1996) (Pubitemid 126515079)
    • (1996) Electronics Letters , vol.32 , Issue.11 , pp. 945-946
    • Namajunas, A.1    Tamasevicius, A.2
  • 29
    • 77954349568 scopus 로고    scopus 로고
    • Tracking control and synchronization of the new hyperchaotic Liu system via backstepping techniques
    • Njah, A.N.: Tracking control and synchronization of the new hyperchaotic Liu system via backstepping techniques. Nonlinear Dyn. 61, 1-9 (2010)
    • (2010) Nonlinear Dyn. , vol.61 , pp. 1-9
    • Njah, A.N.1
  • 30
    • 0005023935 scopus 로고
    • A simple hyperchaos generator including one ideal diode
    • Saito, T.: A simple hyperchaos generator including one ideal diode. IEICE Trans. Fundam. E75-A, 294-298 (1992)
    • (1992) IEICE Trans. Fundam. , vol.E75-A , pp. 294-298
    • Saito, T.1
  • 31
    • 44649133192 scopus 로고    scopus 로고
    • Hyperchaotic beats and their collapse to the quasiperiodic oscillations
    • ́Sliwa, I., Grygiel, K., Szlachetka, P.: Hyperchaotic beats and their collapse to the quasiperiodic oscillations. Nonlinear Dyn. 53, 13-18 (2008)
    • (2008) Nonlinear Dyn. , vol.53 , pp. 13-18
    • Sliwa, I.1    Grygiel, K.2    Szlachetka, P.3
  • 32
    • 78049452630 scopus 로고    scopus 로고
    • Bifurcations and chaotic dynamics in suspended cables under simultaneous parametric and external excitations
    • Chang, S.M., Li, M.C., Lin,W.W.: Bifurcations and chaotic dynamics in suspended cables under simultaneous parametric and external excitations. Nonlinear Dyn. 62, 623-646 (2010)
    • (2010) Nonlinear Dyn. , vol.62 , pp. 623-646
    • Chang, S.M.1    Li, M.C.2    Lin, W.W.3
  • 33
    • 0036860164 scopus 로고    scopus 로고
    • Hyperchaotic behavior of two bidirectionally Chua's circuits
    • Barbara, Silvano: Hyperchaotic behavior of two bidirectionally Chua's circuits. Int. J. Circuit Theory Appl. 30, 625-637 (2002)
    • (2002) Int. J. Circuit Theory Appl. , vol.30 , pp. 625-637
    • Silvano, B.1
  • 35
    • 0000548789 scopus 로고
    • An equation for hyperchaos
    • Rossler, O.E.: An equation for hyperchaos. Phys. Lett. A 71, 155-157 (1979)
    • (1979) Phys. Lett. A , vol.71 , pp. 155-157
    • Rossler, O.E.1
  • 37
    • 33645149365 scopus 로고    scopus 로고
    • Generating hyperchaotic Lu attractor via state feedback control
    • Chen, A., Lu, J., Lu, J., Yu, S.: Generating hyperchaotic Lu attractor via state feedback control. Physica A 364, 103-110 (2006)
    • (2006) Physica A , vol.364 , pp. 103-110
    • Chen, A.1    Lu, J.2    Lu, J.3    Yu, S.4
  • 38
    • 33646501532 scopus 로고    scopus 로고
    • Hyperchaos evolved from the Liu chaotic system
    • Wang, F.Q., Liu, C.X.: Hyperchaos evolved from the Liu chaotic system. Chin. Phys. 15, 963-968 (2006)
    • (2006) Chin. Phys. , vol.15 , pp. 963-968
    • Wang, F.Q.1    Liu, C.X.2
  • 39
    • 2942653227 scopus 로고    scopus 로고
    • A new chaotic attractor
    • Liu, C., Chen, G.: A new chaotic attractor. Chaos Solitons Fractals 22, 1031-1038 (2004)
    • (2004) Chaos Solitons Fractals , vol.22 , pp. 1031-1038
    • Liu, C.1    Chen, G.2
  • 40
    • 58449088118 scopus 로고    scopus 로고
    • Generating hyper-chaotic attractors via approximate time delayed state feedback
    • Hu, G., Jiang, S.: Generating hyper-chaotic attractors via approximate time delayed state feedback. Int. J. Bifurc. Chaos 18, 3485-3494 (2008)
    • (2008) Int. J. Bifurc. Chaos , vol.18 , pp. 3485-3494
    • Hu, G.1    Jiang, S.2
  • 41
    • 34248386538 scopus 로고    scopus 로고
    • Hyperchaos generated from the Lorenz chaotic system and its control
    • Jia, Q.: Hyperchaos generated from the Lorenz chaotic system and its control. Phys. Lett. A 366, 217-222 (2007)
    • (2007) Phys. Lett. A , vol.366 , pp. 217-222
    • Jia, Q.1
  • 42
    • 34347230968 scopus 로고    scopus 로고
    • A hyperchaotic Lorenz attractor and its circuit implementation
    • Wang, G.: A hyperchaotic Lorenz attractor and its circuit implementation. Acta Phys. Sin. 56, 3113-3120 (2007) (Pubitemid 47007124)
    • (2007) Wuli Xuebao/Acta Physica Sinica , vol.56 , Issue.6 , pp. 3113-3120
    • Wang, G.-Y.1    Zheng, Y.2    Liu, J.-B.3
  • 44
    • 0003877443 scopus 로고
    • Harvard University Press, Cambridge
    • Cohen, I.B.: Revolution in Science, p. 467. Harvard University Press, Cambridge (1985, 1994)
    • (1985) Revolution in Science , pp. 467
    • Cohen, I.B.1
  • 45
    • 84863984531 scopus 로고    scopus 로고
    • http://www.wired.com/medtech/genetics/magazine/17-07/ff-originofspecies
  • 46
    • 56649086408 scopus 로고    scopus 로고
    • When Lyapunov exponents fail to exist
    • Ott, W., Yorke, J.A.: When Lyapunov exponents fail to exist. Phys. Rev. E 78, 3755-3763 (2008)
    • (2008) Phys. Rev. E , vol.78 , pp. 3755-3763
    • Ott, W.1    Yorke, J.A.2
  • 47
    • 57849138268 scopus 로고    scopus 로고
    • Hyperchaos of four state autonomous system with three positive Lyapunov exponents
    • Ge, Z.M., Yang, C.H.: Hyperchaos of four state autonomous system with three positive Lyapunov exponents. Phys. Lett. A 373(3), 349-353 (2009)
    • (2009) Phys. Lett. A , vol.373 , Issue.3 , pp. 349-353
    • Ge, Z.M.1    Yang, C.H.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.