Abstract
Secure communication is essential in all fields in our day to life. While the communication, the error occurs due to some circumstance. To rectify that many methodologies are adopted. The hybrid phase synchronization is one of the new techniques to be used in secure communication. This synchronization technique is helpful in such an area. This article is exposed the generalized chaotic system of stretch, twist, fold flow for fractional order. The stability and chaotic nature of the system are examined. This article examined synchronization via a suitable control function. The evaluation process is done to be the consistency of the proposed system. Hybrid phase synchronization is investigated for the indistinguishable chaotic system of stretch, twist and fold flow. The entire synchronization and anti-synchronization is taken to control the system by employing feedback technique. To validate the proposed theory, numerical simulation is presented. The chaotic nature of the system is presented through MATLAB software.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Vainshtein, S.I., R.Z. Sagdeev, R. Rosner, and E.J. Kim. 1996. Fractal properties of the stretch-twist-fold magnetic dynamo. Physical Review E 53 (5): 4729.
Vainshtein, S.I., R.Z. Sagdeev, and R. Rosner. 1997. Stretch-twist-fold and ABC nonlinear dynamos: Restricted chaos. Physical Review E 56 (2): 1605.
Nain, A.K., R.K. Vats, and A. Kumar. 2021. Caputo-Hadamard fractional differential equation with impulsive boundary conditions. Journal of Mathematical Modeling 9 (1): 93–106.
Liu, W., and G. Chen. 2003. A new chaotic system and its generation. International Journal of Bifurcation and Chaos 13 (01): 261–267.
Abdelouahab, M.S., and N.E. Hamri. 2012. A new chaotic attractor from hybrid optical bistable system. Nonlinear Dynamics 67 (1): 457–463.
Wang, Z. 2010. Chaos synchronization of an energy resource system based on linear control. Nonlinear Analysis: Real World Applications 11 (5): 3336–3343.
Wu, X., and S. Li. 2012. Dynamics analysis and hybrid function projective synchronization of a new chaotic system. Nonlinear Dynamics 69 (4): 1979–1994.
Muthukumar, P., and P. Balasubramaniam. 2013. Feedback synchronization of the fractional order reverse butterfly-shaped chaotic system and its application to digital cryptography. Nonlinear Dynamics 74 (4): 1169–1181.
Petráš, I. 2006. Method for simulation of the fractional order chaotic systems. Acta Montanistica Slovaca 11 (4): 273–277.
Jun-Jie, L., and L. Chong-Xin. 2007. Realization of fractional-order Liu chaotic system by circuit. Chinese Physics 16 (6): 1586.
Qiang, H., L. Chong-Xin, S. Lei, and Z. Da-Rui. 2013. A fractional order hyperchaotic system derived from a Liu system and its circuit realization. Chinese Physics B 22 (2): 020502.
Park, J.H., and O.M. Kwon. 2003. A novel criterion for delayed feedback control of time-delay chaotic systems. Chaos, Solitons and Fractals 17: 709–716.
Lu, J., X. Wu, X. Han, and J. Lu. 2004. Adaptive feedback synchronization of a unified chaotic system. Physics Letters A 329: 327–333.
Childress, S., and A.D. Gilbert. 1995. Stretch, Twist, Fold: The Fast Dynamo. Springer Science & Business Media.
Nagaram, N.B., S. Rasappan, and N. K. Jothi. 2019. The backstepping control technique to break-up the life cycle of plasmodium parasite. In AIP Conference Proceedings, Tamil Nadu, India. 020017_1–020017_7.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Nagaram, N.B., Rasappan, S., Murugesan, R., Mohan, K.R., Hachimi, H. (2022). Hybrid Phase Synchronization for Generalized Stretch, Twist, Fold Flow Chaotic System of Fractional Order. In: Peng, SL., Lin, CK., Pal, S. (eds) Proceedings of 2nd International Conference on Mathematical Modeling and Computational Science. Advances in Intelligent Systems and Computing, vol 1422. Springer, Singapore. https://doi.org/10.1007/978-981-19-0182-9_17
Download citation
DOI: https://doi.org/10.1007/978-981-19-0182-9_17
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-19-0181-2
Online ISBN: 978-981-19-0182-9
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)