Applications of an integral sliding mode control for secure digital data communication and synchronization of fractional order 5D non-Hamiltonian conservative hyperchaotic systems

T. Suganya; P. Muthukumar

doi:10.5269/bspm.78485

T. Suganya
P. Muthukumar Gobi Arts & Science College

Abstract

A conservative hyperchaotic system with fractional order in five dimensions is proposed in this study. It is found that the system is conservative but not Hamiltonian. By widening the scope of dynamical analysis, this work advances the understanding of non-Hamiltonian conservative systems. Integral sliding mode control is also used to synchronize conservative hyperchaotic systems of fractional order that are not Hamiltonian. An innovative safe digital data transfer algorithm is created using synchronized fractional order non-Hamiltonian conservative hyperchaotic systems. Numerical simulations verify the accuracy and effectiveness of theoretical conclusions.

Downloads

Download data is not yet available.

References

Boccaletti, S., Grebogi, C., Lai, Y.-C., Mancini,H.,Maza,D., The control of chaos: theory and applications, Physics reports 329(3), 103–197, (2000).

Levy, David, Chaos theory and strategy: Theory, application, and managerial implications, Strategic management journal 15(S2), 167–178, (1994).

A. B. Cambel, Applied chaos theory: A paradigm for complexity, Elsevier, (1993).

G. Qi, G. Chen, S. Li, Y. Zhang, Four-wing attractors: from pseudo to real, International journal of bifurcation and chaos 16(04), 859–885, (2006).

B. Bao, T. Jiang, Q. Xu, M. Chen, H. Wu, Y. Hu, Coexisting infinitely many attractors in active band-pass filter-based memristive circuit, Nonlinear Dynamics 86, 1711–1723, (2016).

J. Yang, Z. Feng, Z. Liu, A new five-dimensional hyperchaotic system with six coexisting attractors, Qualitative Theory of Dynamical Systems 20, 1–31, (2021).

S Vaidyanathan, C Volos, Analysis and adaptive control of a novel 3-D conservative no-equilibrium chaotic system, Archives of Control Sciences 25(3), 333–353, (2015).

G. Qi, J. Hu, Z. Wang, Modeling of a Hamiltonian conservative chaotic system and its mechanism routes from periodic to quasiperiodic, chaos and strong chaos, Applied Mathematical Modelling 78, 350–365, (2020).

P. Muthukumar, P. Balasubramaniam, K. Ratnavelu, Fast projective synchronization of fractional order chaotic and reverse chaotic systems with its application to an affine cipher using date of birth (DOB), Nonlinear Dynamics 80, 1883–1897, (2015).

G. Qi, Modelings and mechanism analysis underlying both the 4D Euler equations and Hamiltonian conservative chaotic systems, Nonlinear Dynamics 95(3), 2063–2077, (2019).

S. Cang, A.Wu, Z.Wang, Z. Chen, Four-dimensional autonomous dynamical systems with conservative flows: two-case study, Nonlinear Dynamics 89, 2495–2508, (2017).

E. Dong, M. Yuan, S. Du, Z. Chen, A new class of Hamiltonian conservative chaotic systems with multistability and design of pseudo-random number generator, Applied Mathematical Modelling 73, 40–71, (2019).

M Lakshmanan, S Rajaseekar, Nonlinear dynamics: integrability, chaos and patterns,(2012).

E. Ott, Chaos in dynamical systems, 2002.

H. Cheng, H. Li, Q. Dai and J. Yang,A deep reinforcement learning method to control chaos synchronization between two identical chaotic systems,Chaos, Solitons & Fractals, 174, 113809, 2023.

Y. Wu, J. L¨u, Dynamics and control of a new chaotic system with hidden attractor, Nonlinear Dynamics 85(2), 1335–1344, (2016).

S. G. Chen, W. Li, An example of a hamiltonian system and controlling chaos with simple limiters, Acta Physica 50(8), 1434-1439, (2001).

T. Ganesan, S. Vaidyanathan, Analysis, adaptive control and synchronization of a new 3-D chaotic system with a curve of equilibrium points, International Journal of Control Theory and Applications 8(3), 869–877, (2015).

K. Murali, M. Lakshmanan, Transmission of signals by synchronization in a chaotic van der Pol–Duffing oscillator, Physical Review E 48(3), R1624, (1993).

X. Leng, Y. Wang, J. Liu, A new chaotic system without equilibrium point, Nonlinear Dynamics 70(2), 1275–1281, (2012).

X. Sun, J. Zhao, B. Du, A novel five-dimensional non-hamiltonian conservative hyperchaotic system with multiple amplitude-modulated behaviors, AEU-International Journal of Electronics and Communications 183, 1553576, (2024).

B. Tian, Q. Peng, X. Leng, B. Du, A new 5d fractional order conservative hyperchaotic system, Physica Scripta 98(1), 015207, (2022).

S. H. Yuningsih et. al., Investigation of chaos behavior and integral sliding mode control on financial risk model, AIMS Mathematics 7(10), 18377-18392, (2022).

C. Xu, K. Sun, S. He, S. Chen, A new 4D chaotic system with hidden attractor and its circuit implementation, Nonlinear Dynamics 93(4), 2291–2302, (2018).

A. Sambas, et. at., A 3d chaotic system with line equilibrium: multistability, integral sliding mode control, electronic circuit, fpga implementation and its image encryption, IEEE Access 10, 68057-68074, (2022).

J C. Sprott, Some simple chaotic flows, Physical Review E 50(2), R647, (1994).

A. Gholipour, M. Nazari, A new chaotic system without equilibrium point and its circuit implementation, International Journal of Bifurcation and Chaos 29(06), 1950082, (2019).

R. Buizza, Chaos and weather prediction, ECMWF Newsletter 106, 6–14, (2006).

Berkovitz, Joseph, Action at a distance in quantum mechanics, Stanford Encyclopedia of Philosophy, (2018).

A. V. Holden, M. Markus, Chaos in biological systems, Springer Science & Business Media, (1986).

M. Thiel, MC. Romano, J. Kurths, How much information is contained in a recurrence plot?, Physics Letters A 330(5), 343–349, (2004).

Li, Chunhua and Yang, Xianfeng, Chaos synchronization of fractional-order hyperchaotic systems, Nonlinear Dynamics 59(4), 575–579, (2010).

A. M. Tusset, M.E.K. Fuziki, J.M. Balthazar, D.I. Andrade and G.G. Lenzi, Dynamic analysis and control of a financial system with chaotic behavior including fractional order, Fractal and Fractional, 7(7), 535, 2023.

Z. Khan, S. Vaidyanathan, VT. Pham, C. Volos, A new fractional order chaotic system with line of equilibria: Dynamical analysis, electronic circuit implementation and applications, The European Physical Journal Special Topics 225, 1303–1313, (2016).

N. Khan, P. Muthukumar, Transient chaos, synchronization and digital image enhancement technique based on a novel 5D fractional-order hyperchaotic memristive system, Circuits, Systems, and Signal Processing 41(4), 2266–2289, (2022).

P. Muthukumar, N. Ramesh Babu, P. Balasubramaniam, Detecting critical point of fractional-order chemical system with synchronization and application to image enhancement technique, Proceedings of the National Academy of Sciences, India Section A: Physical Sciences 91(4), 661–674, (2021).

S.Mohanapriya, P. Muthukumar, EA. Gopalakrishnan, D. Gupta, Active disturbance reduction on non-homogeneous TS fuzzy semi-Markovian jump systems and its application to secure digital signal communication, Chaos, Solitons & Fractals 196, 116275, (2025).

T.Suganya, P. Muthukumar, Projective synchronization of two identical fractional order LLC chaotic systems, Journal of Dynamics and Control 8(10), 46–58, (2024).