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Analysis, Control, and Synchronization of a 3-D Novel Jerk Chaotic System with Two Quadratic Nonlinearities
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  • Journal title : Kyungpook mathematical journal
  • Volume 55, Issue 3,  2015, pp.563-586
  • Publisher : Department of Mathematics, Kyungpook National University
  • DOI : 10.5666/KMJ.2015.55.3.563
 Title & Authors
Analysis, Control, and Synchronization of a 3-D Novel Jerk Chaotic System with Two Quadratic Nonlinearities
VAIDYANATHAN, SUNDARAPANDIAN;
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 Abstract
In this research work, a seven-term 3-D novel jerk chaotic system with two quadratic nonlinearities has been proposed. The basic qualitative properties of the novel jerk chaotic system have been described in detail. Next, an adaptive backstepping controller is designed to stabilize the novel jerk chaotic system with two unknown parameters. Moreover, an adaptive backstepping controller is designed to achieve complete chaos synchronization of the identical novel jerk chaotic systems with two unknown parameters. MATLAB simulations have been shown in detail to illustrate all the main results developed for the 3-D novel jerk chaotic system.
 Keywords
Chaos;jerk system;novel system;adaptive control;backstepping control;chaos synchronization;
 Language
English
 Cited by
1.
A novel 3-D jerk chaotic system with three quadratic nonlinearities and its adaptive control, Archives of Control Sciences, 2016, 26, 1  crossref(new windwow)
2.
Analysis, Adaptive Control and Synchronization of a Novel 4-D Hyperchaotic Hyperjerk System via Backstepping Control Method, Archives of Control Sciences, 2016, 26, 3  crossref(new windwow)
 References
1.
H. N. Agiza and M. T. Yassen, Synchronization of Rossler and Chen chaotic dynamical systems using active control, Physics Letters A, 278(2001), 191-197. crossref(new window)

2.
K. T. Alligood, T. D. Sauer and J. A. Yorke, Chaos: An introduction to Dynamical Systems, Springer, New York, 2000.

3.
A. Arneodo, P. Coullet and C. Tresser, Possible new strange attractors with spiral structure, Communications in Mathematical Physics, 79(1981), 573-579. crossref(new window)

4.
V. Astakhov, A. Shabunin and V. Anishchenko, Antiphase synchronization in symmetrically coupled self-oscillators, International Journal of Bifurcation and Chaos, 10(2000), 849-857.

5.
G. L. Baker and J. P. Gollub, Chaotic Dynamics: An Introduction, Cambridge University Press, New York, 1990.

6.
G. Cai and Z. Tan, Chaos synchronization of a new chaotic system via nonlinear control, Journal of Uncertain Systems, 1(2007), 235-240.

7.
G. Cai and W. Tu, Adaptive backstepping control of the uncertain unified chaotic system, International Journal of Nonlinear Science, 4(2007), 17-24.

8.
G. Chen and T. Ueta, Yet another chaotic attractor, International Journal of Bifurcation and Chaos, 9(1999), 1465-1466. crossref(new window)

9.
M. J. Feigenbaum, Universal behaviour in nonlinear systems, Physica D: Nonlinear Phenomena, 7(1983), 16-39.

10.
H. Fujisaka and T. Yamada, Stability theory of synchronized motion in coupled-oscillator systems, Progress of Theoretical Physics, 69(1983), 32-47. crossref(new window)

11.
H. P. W. Gottlieb, Question # 38. What is the simplest jerk function that gives chaos? American Journal of Physics, 64(1996), 525.

12.
B. A. Idowu, U. E. Vincent and A. N. Njah, Synchronization of chaos in non-identical parametrically excited systems, Chaos, Solitons and Fractals, 39(2009), 2322-2331. crossref(new window)

13.
S. Jafari and J. C. Sprott, Simple chaotic flows with a line equilibrium, Chaos, Solitons and Fractals, 57(2013), 79-84. crossref(new window)

14.
T. Kapitaniak, Controlling Chaos: Theoretical and Practical Methods in Non-linear Dynamics, Academic Press, New York, 1996.

15.
R. Karthikeyan and V. Sundarapandian, Hybrid chaos synchronization of four-scroll systems via active control, Journal of Electrical Engineering, 65(2014), 97-103.

16.
M. Lakshmanan and K. Murali, Chaos in Nonlinear Oscillators: Controlling and Synchronization, World Scientific, Singapore, 1996.

17.
D. Li, A three-scroll chaotic attractor, Physics Letters A, 372(2008), 387-393. crossref(new window)

18.
C. X. Liu, T. Liu, L. Liu and K. Liu, A new chaotic attractor, Chaos, Solitons and Fractals, 22(2004), 1031-1038. crossref(new window)

19.
E. N. Lorenz, Deterministic nonperiodic flow, Journal of the Atmospheric Sciences, 20(1963), 130-141. crossref(new window)

20.
J. Lu and G. Chen, A new chaotic attractor coined, International Journal of Bifurcation and Chaos, 12(2002), 659-661. crossref(new window)

21.
R. Mainieri and J. Rehacek, Projective synchronization in three-dimensional chaotic system, Physical Review Letters, 82(1999), 3042-3045. crossref(new window)

22.
R. M. May, Limit cycles in predator-prey communities, Science, 177(1972), 900-908. crossref(new window)

23.
M. C. Pai, Global synchronization of uncertain chaotic systems via discrete-time sliding mode control, Applied Mathematics and Computation, 227(2014), 663-671. crossref(new window)

24.
L. M. Pecora and T. L. Caroll, Synchronization in chaotic systems, Physical Review Letters, 64(1990), 821-825. crossref(new window)

25.
I. Pehlivan, I. M. Moroz and S. Vaidyanathan, Analysis, synchronization and circuit design of a novel butterfly attractor, Journal of Sound and Vibration, 333(2014), 5077-5096. crossref(new window)

26.
V. T. Pham, C. Volos, S. Jafari, Z. Wei and X. Wang, Constructing a novel noequilibrium chaotic system, International Journal of Bifurcation and Chaos, 24(2014), 1450073. crossref(new window)

27.
A. S. Pikovsky, M. G. Rosenblum and J. Kurths, Synchronization: A Unified Concept in Nonlinear Sciences, Cambridge University Press, New York, 2001.

28.
S. Rasappan and S. Vaidyanathan, Global chaos synchronization of WINDMI and Coullet chaotic systems by backstepping control, Far East Journal of Mathematical Sciences, 67(2012), 265-287.

29.
S. Rasappan and S. Vaidyanathan, Hybrid synchronization of n-scroll Chua circuits using adaptive backstepping control design with recursive feedback, Malaysian Journal of Mathematical Sciences, 7(2013), 219-226.

30.
S. Rasappan and S. Vaidyanathan, Global chaos synchronization of WINDMI and Coullet chaotic systems using adaptive backstepping control design, Kyungpook Math. J., 54(2014), 293-320. crossref(new window)

31.
M. G. Rosenblum, A. S. Pikovsky and J. Kurths, Phase synchronization of chaotic oscillators, Physical Review Letters, 76(1996), 1804-1807. crossref(new window)

32.
M. G. Rosenblum, A. S. Pikovsky and J. Kurths, From phase to lag synchronization in coupled chaotic oscillators, Physical Review Letters, 78(1997), 4193-4196. crossref(new window)

33.
O. E. Rossler, An equation for continuous chaos, Physics Letters A, 57(1976), 397-398. crossref(new window)

34.
D. Ruelle and F. Takens, On the nature of turbulence, Communications in Mathematical Physics, 20(1971), 167-192. crossref(new window)

35.
N. F. Rulkov, M. M. Sushchik, L. S. Tsimring and H. D. I. Ababarnel, Generalized synchronization of chaos in directionally coupled chaotic systems, Physical Review E, 51(1995), 980-994. crossref(new window)

36.
P. Sarasu and V. Sundarapandian, The generalized projective synchronization of hyperchaotic Lorenz and hyperchaotic Qi systems via active control, International Journal of Soft Computing, 6(2011), 216-223. crossref(new window)

37.
P. Sarasu and V. Sundarapandian, Adaptive controller design for the generalized projective synchronization of 4-scroll systems, International Journal of Signal System Control and Engineering Application, 5(2012), 21-30.

38.
P. Sarasu and V. Sundarapandian, Generalized projective synchronization of threescroll chaotic systems via adaptive control, European Journal of Scientific Research, 72(2012), 504-522.

39.
J. C. Sprott, Some simple chaotic flows, Physical Review E, 50(1994), 647-650. crossref(new window)

40.
J. C. Sprott, Some simple chaotic jerk functions, American Journal of Physics, 65(1997), 537-543. crossref(new window)

41.
J. C. Sprott, A new class of chaotic circuit, Physics Letters A, 266(2000), 19-23. crossref(new window)

42.
J. C. Sprott, Chaos and Time-Series Analysis, Oxford University Press, Oxford, 2003.

43.
J. C. Sprott, Elegant Chaos, World Scientific, Singapore, 2010.

44.
V. Sundarapandian, Analysis and anti-synchronization of a novel chaotic system via active and adaptive controllers, Journal of Engineering Science and Technology Review, 6(2013), 45-52.

45.
V. Sundarapandian and R. Karthikeyan, Anti-synchronization of hyperchaotic Lorenz and hyperchaotic Chen systems by adaptive control, International Journal of Signal System Control and Engineering Application, 4(2011), 18-25.

46.
V. Sundarapandian and R. Karthikeyan, Anti-synchronization of Lu and Pan chaotic systems by adaptive nonlinear control, International Journal of Soft Computing, 6(2011), 111-118. crossref(new window)

47.
V. Sundarapandian and R. Karthikeyan, Anti-synchronization of Lu and Pan chaotic systems by adaptive nonlinear control, European Journal of Scientific Research, 64(2011), 94-106.

48.
V. Sundarapandian and R. Karthikeyan, Adaptive anti-synchronization of uncertain Tigan and Li Systems, Journal of Engineering and Applied Sciences, 7(2012), 45-52. crossref(new window)

49.
V. Sundarapandian and R. Karthikeyan, Hybrid synchronization of hyperchaotic Lorenz and hyperchaotic Chen systems via active control, Journal of Engineering and Applied Sciences, 7(2012), 254-264. crossref(new window)

50.
V. Sundarapandian and I. Pehlivan, Analysis, control, synchronization and circuit design of a novel chaotic system, Mathematical and Computer Modelling, 55(2012), 1904-1915. crossref(new window)

51.
V. Sundarapandian and S. Sivaperumal, Sliding controller design of hybrid synchronization of four-wing chaotic systems, International Journal of Soft Computing, 6(2011), 224-231. crossref(new window)

52.
R. Suresh and V. Sundarapandian, Global chaos synchronization of a family of n-scroll hyperchaotic Chua circuits using backstepping control with recursive feedback, Far East Journal of Mathematical Sciences, 73(2013), 73-95.

53.
X. Tan, J. Zhang and Y. Yang, Synchronizing chaotic systems using backstepping design, Chaos, Solitons and Fractals, 16(2003), 37-45. crossref(new window)

54.
G. Tigan and D. Opris, Analysis of a 3D chaotic system, Chaos, Solitons and Fractals, 36(2008), 1315-1319. crossref(new window)

55.
S. Vaidyanathan, Anti-synchronization of Sprott-I and Sprott-M chaotic systems via adaptive control, International Journal of Control Theory and Applications, 5 (2012), 41-59.

56.
S. Vaidyanathan, Global chaos control of hyperchaotic Liu system via sliding control method, International Journal of Control Theory and Applications, 5(2012), 117-123.

57.
S. Vaidyanathan, Adaptive backstepping controller and synchronizer design for Arneodo chaotic system with unknown parameters, International Journal of Computer Science and Information Technology, 4(2012), 145-159. crossref(new window)

58.
S. Vaidyanathan, A new six-term 3-D chaotic system with an exponential nonlinearity, Far East Journal of Mathematical Sciences, 79(2013), 135-143.

59.
S. Vaidyanathan, Analysis and adaptive synchronization of two novel chaotic systems with hyperbolic sinusoidal and cosinusoidal nonlinearity and unknown parameters, Journal of Engineering Science and Technology Review, 6(2013), 53-65.

60.
S. Vaidyanathan, A new eight-term 3-D polynomial chaotic system with three quadratic nonlinearities, Far East Journal of Mathematical Sciences, 84(2014), 219-226.

61.
S. Vaidyanathan, Analysis, control and synchronisation of a six-term novel chaotic system with three quadratic nonlinearities, International Journal of Modelling, Identi fication and Control, 22(2014), 41-53. crossref(new window)

62.
S. Vaidyanathan, Analysis and adaptive synchronization of eight-term 3-D polynomial chaotic systems with three quadratic nonlinearities, European Physical Journal: Special Topics, 223(2014), 1519-1529.

63.
S. Vaidyanathan, Global chaos synchronisation of identical Li-Wu chaotic systems via sliding mode control, International Journal of Modelling, Identification and Control, 22(2014), 170-177. crossref(new window)

64.
S. Vaidyanathan and K. Madhavan, Analysis, adaptive control and synchronization of a seven-term novel 3-D chaotic system, International Journal of Control Theory and Applications, 6(2013), 121-137.

65.
S. Vaidyanathan and S. Pakiriswamy, Generalized projective synchronization of sixterm Sundarapandian chaotic systems by adaptive control, International Journal of Control Theory and Applications, 6(2013), 153-163.

66.
S. Vaidyanathan and K. Rajagopal, Hybrid synchronization of hyperchaotic Wang-Chen and hyperchaotic Lorenz systems by active non-linear control, International Journal of Signal System Control and Engineering Application, 4(2011), 55-61.

67.
S. Vaidyanathan and K. Rajagopal, Global chaos synchronization of hyperchaotic Pang and hyperchaotic Wang systems via adaptive control, International Journal of Soft Computing, 7(2012), 28-37. crossref(new window)

68.
S. Vaidyanathan and S. Rasappan, Global chaos synchronization of n-scroll Chua circuit and Lur'e system using backstepping control design with recursive feedback, Arabian Journal for Science and Engineering, 39(2014), 3351-3364. crossref(new window)

69.
S. Vaidyanathan and S. Sampath, Anti-synchronization of four-wing chaotic systems via sliding mode control, International Journal of Automatic Computing, 9(2012), 274-279. crossref(new window)

70.
S. Vaidyanathan, C. Volos, V.T. Pham, K. Madhavan and B.A. Idowu, Adaptive backstepping control, synchronization and circuit simulation of a 3-D novel jerk chaotic system with two hyperbolic sinusoidal nonlinearities, Archives of Control Sciences, 24(2014), 257-285.

71.
U. E. Vincent, Synchronization of identical and non-identical 4-D chaotic systems using active control, Chaos, Solitons and Fractals, 37(2008), 1065-1075. crossref(new window)

72.
M. T. Yassen, Controlling, synchronization and tracking chaotic Liu system using active backstepping design, Physics Letters A, 360(2007), 582-587. crossref(new window)

73.
D. Zhang and J. Xu, Projective synchronization of different chaotic time-delayed neural networks based on integral sliding mode controller, Applied Mathematics and Computation, 217(2010), 164-174. crossref(new window)