Fractional Order of a New 7D Hyperchaotic Lorenz-like System

Key Findings & Data:Numerical implementations of this proposed system with specific parameters are investigated and compared with the new 7D continuous hyperchaotic system.

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Conclusion & Impact:Numerical analysis of Lyapunov exponents verifies the existence of hyperchaos for less than five orders.

🔬Design:Research Article

📍Scope:Comprehensive Sample

⚙️Variables:Chaos · Fractional order derivatives · Fractional stability

Abstract

In this paper, a new 7D hyperchaotic Lorenz-like system is proposed with perspective of fractional order. Numerical implementations of this proposed system with specific parameters are investigated and compared with the new 7D continuous hyperchaotic system. In addition to this, due to the hyperchaotic attractors do not exist lower than 0.6, the values of fractional order are analysed in range between 0.6 to 1. Stability conditions are obtained through the stability theory of fractional systems. Numerical analysis of Lyapunov exponents verifies the existence of hyperchaos for less than five orders.

Keywords

Chaos Fractional order derivatives Fractional stability Hyperchaos Lorenz-like system Lyapunov exponents

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Cite This Article

HASPOLAT, E., YILDIZ, B. (2021). Fractional Order of a New 7D Hyperchaotic Lorenz-like System. Konuralp Journal of Mathematics, Cilt: 9 - Sayı: 1, 76–89. https://ajindex.com/articles/786400

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References (16)

Arena, P., Baglio, S., Fortuna, L., and Manganaro, G. (1995). Hyperchaos from cellular neural networks. Electronics letters, 31(4):250–251
Benettin, G., Galgani, L., Giorgilli, A., and Strelcyn, J.-M. (1980). Lyapunov characteristic exponents for smooth dynamical systems and for hamiltonian systems; a method for computing all of them. part 1: Theory. Meccanica, 15(1):9–20
Cannas, B. and Cincotti, S. (2002). Hyperchaotic behaviour of two bi-directionally chua’s circuits. International Journal of Circuit Theory and Applications, 30:625 – 637
Caputo, M. (1967). Linear models of dissipation whose q is almost frequency independent—ii. Geophysical Journal International, 13(5):529–539
Carpinteri, A. and Mainardi, F. (2014). Fractals and fractional calculus in continuum mechanics, volume 378. Springer
Chen, Z., Yang, Y., Qi, G., and Yuan, Z. (2007). A novel hyperchaos system only with one equilibrium. Physics Letters A, 360(6):696–701
Debnath, L. (2003). Recent applications of fractional calculus to science and engineering. International Journal of Mathematics and Mathematical Sciences, 2003(54):3413–3442
Diethelm, K. and Ford, N. J. (2002). Analysis of fractional differential equations. Journal of Mathematical Analysis and Applications, 265(2):229–248
Diethelm, K., Ford, N. J., and Freed, A. D. (2002). A predictor-corrector approach for the numerical solution of fractional differential equations. Nonlinear Dynamics, 29(1-4):3–22
Duan, J.-S. (2005). Time-and space-fractional partial differential equations. Journal of mathematical physics, 46(1):013504
Farghaly, A. and Shoreh, A. (2018). Some complex dynamical behaviors of the new 6d fractional-order hyperchaotic lorenz-like system. Journal of the Egyptian Mathematical Society, 26(1):138–155
Garrappa, R. (2011). Predictor-corrector pece method for fractional differential equations. MATLAB Central File Exchange
Hartley, T. T., Lorenzo, C. F., and Qammer, H. K. (1995). Chaos in a fractional order chua’s system. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 42(8):485–490
Hilfer, R. et al. (2000). Applications of fractional calculus in physics, volume 35. World scientific Singapore
Hsieh, J.-Y., Hwang, C.-C., Wang, A.-P., and Li, W.-J. (1999). Controlling hyperchaos of the rossler system. International Journal of Control, 72(10):882–886
Huang, X., Zhao, Z., Wang, Z., and Li, Y. (2012). Chaos and hyp