Complete synchronization, phase synchronization and parameters estimation in a realistic chaotic system

Communications in Nonlinear Science and Numerical Simulation

Volumn 16, Issue 9, 2011, Pages 3770-3785

  Ma, Jun ^a,b   Li, Fan ^a   Huang, Long ^a   Jin, Wu Yin ^a  

^a LANZHOU UNIVERSITY OF TECHNOLOGY   (China)

^b KEY LABORATORY OF GANSU ADVANCED CONTROL FOR INDUSTRIAL PROCESSES   (China)

Author keywords

Complete synchronization; Jacobi matrix; Parameter estimation; Phase synchronization

Indexed keywords

CHAOTIC SYSTEMS; EIGENVALUES AND EIGENFUNCTIONS; JACOBIAN MATRICES; LYAPUNOV FUNCTIONS; SYNCHRONIZATION;

CHAOTIC PROPERTIES; CHAOTIC REGIONS; COMPLETE SYNCHRONIZATION; JACOBI MATRIX; PARAMETERS ESTIMATION; PHASE PARAMETERS; PHASE SPACES; PHASE SYNCHRONIZATION; SYNCHRONIZATION ESTIMATION; TWO PARAMETER;

PARAMETER ESTIMATION;

EID: 79953697084     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2010.12.030     Document Type: Article

References (72)

1. Misra J. Phase synchronization. Inf Process Lett 1991, 38(2):101-105.
2. Pikovsky A.S., Rosenblum M.G., Osipov G.V., Kurths J. Phase synchronization of chaotic oscillators by external driving. Physica D 1997, 104(3-4):219-238.
3. Shuai J.W., Durand D.M. Phase synchronization in two coupled chaotic neurons. Phys Lett A 1999, 264(4):289-297.
4. Boccaletti S., Kurths J., Osipov G., Valladares D.L., Zhou C.S. The synchronization of chaotic systems. Phys Report 2002, 336:1-101.
5. Ávila G.M.R., Guisset J.L., Deneubourg J.L. Synchronization in light-controlled oscillators. Physica D 2003, 182(3-4):254-273.
6. Perc M., Marhl M. Sensitivity and flexibility of regular and chaotic calcium oscillations. Biophys Chem 2003, 104:509-522.
7. Perc M., Marhl M. Detecting and controlling unstable periodic orbits that are not part of a chaotic attractor. Phys Rev E 2004, 70:016204.
8. Belykh V.N., Osipov G.V., Kuckländer N., Blasius B., Kurths J. Automatic control of phase synchronization in coupled complex oscillators. Physica D 2005, 200(1-2):81-104.
9. Wu D., Jia Y., Yang L.J., Liu Q., Zhan X. Phase synchronization and coherence resonance of stochastic calcium oscillations in coupled hepatocytes. Biophys Chem 2005, 115(1):37-47.
10. Perc M. Visualizing the attraction of strange attractors. Eur J Phys 2005, 26:579-587.
11. Perc M. Nonlinear time series analysis of the human electrocardiogram. Eur J Phys 2005, 26:757-768.
12. Alatriste F.R., Mateos J.L. Phase synchronization in tilted deterministic ratchets. Physica A 2006, 372(2):263-271.
13. Nikulin V.V., Brismar T. Phase synchronization between alpha and beta oscillations in the human electroencephalogram. Neuroscience 2006, 137(2):647-657.
14. Wei D.Q., Luo X.S. Adaptive robust control of chaotic oscillations in power system with excitation limits. Chin Phys B 2007, 16(11):3244-3248.
15. Wei D.Q., Zhang B. Controlling chaos in permanent magnet synchronous motor based on finite-time stability theory. Chin Phys B 2009, 18(4):1399-1403.
16. Liu L., Su Z.C., Liu C.X. A new chaotic system and its circuit simulation. Acta Phys Sin 2007, 56(4):1966-1970.
17. Miliou A.N., Antoniades I.P., Stavrinides S.G., Anagnostopoulos A.N. Secure communication by chaotic synchronization: robustness under noisy conditions. Nonlinear Anal B 2007, 8(3):1003-1012.
18. Denker M., Roux S., Timme M., Riehle A., Grün S. Phase synchronization between LFP and spiking activity in motor cortex during movement preparation. Neurocomputer 2007, 70(10-12):2096-2101.
19. Kim C.S., Riikonen P., Salakoski T. Detecting biological associations between genes based on the theory of phase synchronization. Biosystems 2008, 92(2):99-113.
20. Bob P., Palus M., Susta M., Glaslova K. EEG phase synchronization in patients with paranoid schizophrenia. Neurosci Lett 2008, 447(1):73-77.
21. Erjaee G.H., Momani S. Phase synchronization in fractional differential chaotic systems. Phys Lett A 2008, 372(14):2350-2354.
22. Choi YP, Ha SY, Yun SB. Complete synchronization of Kuramoto oscillators with finite inertia. Physica D. doi:10.1016/j.physd.2010.08.004.
23. Handbook of chaos control 2007, Wiley-VCH Verlag Gmbh. E. Schöll, H.G. Schuster (Eds.).
24. Recent progress in controlling chaos 2010, World Scientific, Singapore. M.A.F. Sanjuan, C. Grebogi (Eds.).
25. Ma J., Ying H.P., Liu Y., Li S.R. Development and transition of spiral wave in the coupled Hindmarsh-Rose neurons in two-dimensional space. Chin Phys B 2009, 18(1):98-105.
26. Ma J., Zhang A.H., Tang J., Jin W.Y. Collective behaviors of spiral wave in the networks of Hodgkin-Huxley neurons in presence of channel noise. J Biol Syst 2010, 18(1):243-259.
27. Ma J., Yang L.J., Wu Y., Zhang C.R. Spiral wave in small-world networks of Hodgkin-Huxley neurons. Commun Theor Phys 2010, 54(3):583-588.
28. Wang M.S., Hou Z.H., Xin H.W. Ordering spatiotemporal chaos in small-world neuron networks. ChemPhysChem 2006, 7:579.
29. Hou Z.H., Xin H.W. Noise sustained spiral waves: effects of spatial and temporal memory. Phys Rev Lett 2002, 89:280601.
30. Nadkarni S., Jung P. Spontaneous oscillations of dressed neurons: a new mechanism for epilepsy?. Phys Rev Lett 2003, 91(26):268101.
31. Wang Q.Y., Duan Z.S., Perc M., Chen G.R. Synchronization transitions on small-world neuronal networks: effects of information transmission delay and rewiring probability. Europhys Lett 2008, 83:50008.
32. Wang Q.Y., Perc M., Chen G.R. Synchronization transitions on scale-free neuronal networks due to finite information transmission delays. Phys Rev E 2009, 80:026206.
33. Perc M. Stochastic resonance on excitable small-world networks via a pacemaker. Phys Rev E 2007, 76:066203.
34. Gosak M., Perc M. Proximity to periodic windows in bifurcation diagrams as a gateway to coherence resonance in chaotic systems. Phys Rev E 2007, 76:037201.
35. Long M., Qiu S.S., Peng F. Bi-directional secure communication based on discrete chaotic synchronization. Commun Theor Phys 2007, 47(6):1076-1080.
36. Banerjee S., Chowdhury A.R. Functional synchronization and its application to secure communications. Int J Modern Phys B 2009, 23(9):2285-2295.
37. Irving A.D., Dewson T. Volterra functional secure communication systems. Int J Bifur Chaos 2003, 13(1):123-146.
38. Andrievsky B. Adaptive synchronization methods for signal transmission on chaotic carriers. Math Comput Simul 2002, 58(4-6):285-293.
39. Wang Q.Y., Lu Q.S., Wang H.X. Transition to complete synchronization via nearly synchronization in two coupled chaotic neurons. Chin Phys 2005, 14(11):2189-2195.
40. Shahverdiev E.M., Sivaprakasam S., Shore K.A. Lag synchronization in time-delayed systems. Phys Lett A 2002, 292(6):320-324.
41. Li C.D., Liao X.F., Wong K.W. Lag synchronization of hyperchaos with application to secure communications. Chaos Solitons Fractals 2005, 23(1):183-193.
42. Wang Z.L., Shi X.R. Chaotic bursting lag synchronization of Hindmarsh-Rose system via a single controller. Appl Math Comput 2009, 215(3):1091-1097.
43. Wang L.P., Yuan Z.T., Chen X.H., Zhou Z.F. Lag synchronization of chaotic systems with parameter mismatches. Commun Nonlinear Sci Numer Simul 2011, 16(2):987-992.
44. Yang J.Z., Hu G. Three types of generalized synchronization. Phys Lett A 2007, 361(4-5):332-335.
45. Fujisaka H., Yamada T., Kinoshita G., Kono T. Chaotic phase synchronization and phase diffusion. Physica D 2005, 205(1-4):41-47.
46. Ge Z.M., Chen C.C. Phase synchronization of coupled chaotic multiple time scales systems. Chaos Solitons Fractals 2004, 20(3):639-647.
47. Paluš M. Detecting phase synchronization in noisy systems. Phys Lett A 1997, 235(4):341-351. 10.
48. Follmann R., Macau E.E.N., Rosa E. Detecting phase synchronization between coupled non-phase-coherent oscillators. Phys Lett A 2009, 373(25):2146-2153.
49. Tsukamoto N., Fujisaka H. Return map analysis of chaotic phase synchronization. Physica D 2007, 233(1):32-38.
50. Casado J.M. Synchronization of two Hodgkin-Huxley neurons due to internal noise. Phys Lett 2003, A310(5-6):400-406.
51. Zhang X.H., Liao X.F., Li C.D. Impulsive control, complete and lag synchronization of unified chaotic system with continuous periodic switch. Chaos Solitons Fractals 2005, 26(3):845-854.
52. Shu Y.L., Zhang A.B., Tang B.D. Switching among three different kinds of synchronization for delay chaotic systems. Chaos Solitons Fractals 2005, 23(2):563-571.
53. Wang Q.Y., Lu Q.S. Time delay enhanced synchronization and regularization in two coupled chaotic ML neurons. Chin Phys Lett 2005, 22:543-546.
54. Wang Q.Y., Duan Z.S., Feng Z.S., Chen G.R., Lu Q.S. Synchronization transition in gap-junction-coupled leech neurons. Physica A 2008, 387(16-17):4404-4410.
55. Wang Q.Y., Lu Q.S., Chen G.R. Synchronization transition by synaptic delay in coupled fast spiking neurons. Int J Bifur Chaos 2008, 4:1189-1198.
56. Wang Q.Y., Duan Z.S., Perc M., Chen G.R. Synchronization transitions on small-world neuronal networks: effects of information transmission delay and rewiring probability. Europhys Lett 2008, 83:50008.
57. Shi X., Lu Q.S. Burst synchronization of electrically and chemically coupled map-based neurons. Physica A 2009, 388(12):2410-2419.
58. Ho M.C., Hung Y.C., Chou C.H. Phase and anti-phase synchronization of two chaotic systems by using active control. Phys Lett A 2002, 296(1):43-48.
59. Liu J.B., Ye C.F., Zhang S.J., Song W.T. Anti-phase synchronization in coupled map lattices. Phys Lett A 2000, 274(1-2):27-29.
60. El-Dessoky M.M. Anti-synchronization of four scroll attractor with fully unknown parameters. Nonlinear Anal B 2010, 11(2):778-783.
61. Al-sawalha M.M., Noorani M.S.M., Al-dlalah M.M. Adaptive anti-synchronization of chaotic systems with fully unknown parameters. Comput Math Appl 2010, 59(10):3234-3244.
62. Shi X.R., Wang Z.L. Adaptive added-order anti-synchronization of chaotic systems with fully unknown parameters. Appl Math Comput 2009, 215(5):1711-1717.
63. Al-Sawalha M.M., Noorani M.S.M. Anti-synchronization of two hyperchaotic systems via nonlinear control. Commun Nonlinear Sci Numer Simul 2009, 14(8):3402-3411.
64. Al-Sawalha M.M., Noorani M.S.M. Adaptive anti-synchronization of two identical and different hyperchaotic systems with uncertain parameters. Commun Nonlinear Sci Numer Simul 2010, 15(4):1036-1047.
65. Zhang Q., Lü J.H., Chen S.H. Coexistence of anti-phase and complete synchronization in the generalized Lorenz system. Commun Nonlinear Sci Numer Simul 2010, 15(10):3067-3072.
66. Qin W.X., Chen G.R. Coupling schemes for cluster synchronization in coupled Josephson equations. Physica D 2004, 197(3-4):375-391.
67. Asheghan M.M., Beheshti M.T.H., Tavazoei M.S. Robust synchronization of perturbed Chen's fractional-order chaotic systems. Commun Nonlinear Sci Numer Simul 2011, 16(2):1044-1051.
68. Xiao Y.Z., Xu W., Tang S.F., Li X.C. Adaptive complete synchronization of the noise-perturbed two bi-directionally coupled chaotic systems with time-delay and unknown parametric mismatch. Appl Math Comput 2009, 213(2):538-547.
69. Al-sawalha M.M., Noorani M.S.M. Adaptive reduced-order anti-synchronization of chaotic systems with fully unknown parameters. Commun Nonlinear Sci Numer Simul 2010, 15(10):3022-3034.
70. Salarieh H., Alasty A. Adaptive chaos synchronization in Chua's systems with noisy parameters. Math Comput Simul 2008, 79(3):233-241.
71. Krese B., Perc M., Govekar E. The dynamics of laser droplet generation. Chaos 2010, 20:013129.
72. Pikovsky A.S., Rosemblum M., Kurths J. Synchronization: a universal concept in nonlinear sciences 2001, Cambridge University Press, Cambridge, UK.