Original Research Article
Article volume = 2022 and issue = 1
Pages: 23–33
Article publication Date: November 21, 2022
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Encryption and Decryption of a Chaotic Fractional Order Financial System
Malek Karimian
Department of mathematics, university of Ilam, Ilam, Iran.
Abstract:
This paper presents the anti-synchronization of two non-identical chaotic fractional order financial system with disturbance observe (FOFSDO), such that the anti-synchronization is discussed with new parameters and disturbance in slave system by using nonlinear active control technique. The stability of scheme is proved by applying Lyapunov stability method for error system. The result of anti-synchronization with disturbance is applied in cryptography. Numerical examples and simulations analysis show the applicability and validity of the scheme and considered system.
Keywords:
Chaotic, Anti-synchronization, Secure Communication.
References:
- [1] M. Karimian, B. Naderi, Y. Edrisi Tabriz, Application of a afractional-order financial system with disturbance in encryption and decryption. Int. J. Nonlinear Anal. Appl. In press, 1-14, (2022). 1, 2
- [2] C. J. Cheng, Robust synchronization of uncertain unified chaotic systems subject to noise and its application to secure communication, Applied Mathematics and Computation, 219 (2012) 2698-2712. 4
- [3] F. Yua, C. Wang, Secure communication based on a four-wing chaotic system subjectto disturbance inputs. Optik, 125, 5920-5925 (2014). 1
- [4] M. F. Haroun, A. T. Gulliver, A new 3D chaotic cipher for encrypting two data streams simultaneously. Nonlinear Dyn., 81, 1053-1066 (2015). 1
- [5] X. Wang, M. Wang Adaptive synchronization for a class of high-dimensional autonomous uncertain chaotic systems. Int. J. Mod. Phys. C, 18(3), 399-406 (2007). 1
- [6] Y. Xu ., H. Wang, Y. Li, B. Pei, Image encryption based on synchronization of fractional chaotic 1
- [7] C. Tao, X. Liu, Feedback and adaptive control and synchronization of a set of chaotic and hyperchaotic systems. Chaos Solitons Fract., 32(4), 1572-1581 (2007). 1
- [8] M. Rafael, nez-Guerran, J. Juan. Montesinos Garcia, Sergio M. Secure communications via synchronization of Liouvillian chaotic systems, Journal of the Franklin Institute, 353 (2016) 4384-4399. 1
- [9] K. M. Cuomo, A. V. Oppenheim, S. H. Strogatz, Synchronization of Lorenz-based chaotic circuits with applications to communications. IEEE Trans Circuits Syst, 40, 626-33 (1993). 1
- [10] U. Parlitz,L. O. Chua,L. Kocarev,Ks. Halle, A. Shang. Transmission of digital signals by chaotic synchronization. Int. J. Bifur. Chaos, 2, 973-977 (1992). 1
- [11] H. Dedieu, M. P. Kennedy, M. Hasler, Chaos shift keying: modulation and demodulation of a chaotic carrier using self-synchronizing Chua’s circuits. IEEE, Trans Circuits Syst, 40, 634-642 (1993). 1
- [12] T. Yang, L.O. Chua, Secure communication via chaotic parameter modulation. IEEE Trans. Circuits Syst. I, 43, 817-819 (1996). 1
- [13] L. Kocarev K. S. Halle, K. Eckert, L. O. Chua, U. Parlitz, Experimental demonstration of secure communication via chaotic synchronization. Int J Bifur Chaos, 2, 709-713 (1992). 1
- [14] B. Naderi, H. Kheiri, A. Heydari, R.Mahini. Optimal synchronization of complex chaotic t-systems andits application in secure communication. Journal of Control, Automation and Electrical Systems, 27(4), 2016, 379–390. 1
- [15] D. Matignon, Stability results for fractional differential equations with applications to control processing. Computational Engineering in systems Applications, IMACS, IEEESMC, Lille, France, Vol, 2, pp. 963-968 (1996). 2.3
- [16] B. Naderi , H. Kheiri, Exponential synchronization of chaotic system and application in secure communication. Optik - International Journal for Light and Electron Optics, 127(5), 2407–2412 (2016). 1
- [17] Boutayeb M., M. Darouach, H. Rafaralahy, Generalized state observers for chaotic synchronization and secure communication. IEEE Trans Circuits Syst I, 49, 345-346 (2002). 1
- [18] Li. Changpin,D. Weihua, Remarks on fractional derivatives. App. Math. Comput. 187, 777-784(2007) 2, 2
- [19] P. Muthukumar,P. Balasubramaniam, K. Ratnavelu, A novel cascade encryption algorithm for digital images based on anti-synchronization fractional-order dynamical systems. Multimed Tools Appl, DoI 10.1007/s11042- 016-4052-4(2016) 1
- [20] M. Sirvastava, S. K. Agrawal,S. Das, Reduced-order anti-synchronization of the projections of the fractional-order hyperchaotic and chaotic systems. Control European Journal of Physics, DoI 10.2478/s11534-013-0310-5(2013) 1
- [21] H. Taghvafar,G. H. Erjaee, Phase and anti-phase synchronization of fractional-order chaotic systems via active control. Commun Nonlinear Sci Numer Simulat 16, 4079-4088(2011) 1
- [22] Sirvastava, M., Ansari, S.P., Agrawal, S. K.: Anti-synchronization between identical and non-identical fractionalorder chaotic systems wing active control method. Nonlinear Dyn. DoI 10.1007/s11071-013-1171-0(2013) 1
- [23] V. K. Yadav, S. K. Agrawal, M. Sirvestava, S. Das, Phase and anti phase synchronization of fractional-order hyperchaotic systems with uncertainties and external disurbances using nonlinear active method . Int. J. Dynam. Control. DoI 10.1007/s40435-015-0186-X (2015). 1
- [24] B. Bandyopadhyay, S. Kamal, Stabilization and control of fractional-order systems a sliding mode approach. DoI 10.1007/s978-3-319-08621-7, springer(2015). 2.1
- [25] M. M. Sawalla,M. S. M. Noorani, Chaos reduced-order anti-synchronization of chaotic systems with fully unknown parameters. Commun Nonlinear Sci Numer Simulat 17, 1908-1920(2012) 1
- [26] W. Jawadda,M. S. Noorani, M. Al-Sawalla, Robust active sliding mode anti-synchronization of hyperchaotic systems with uncertainties and external disturbances. Nonlinear Analysis: Real word Applications, 13 , 2403-2413(2012) 1
- [27] D. Chen, R. Zhang, X. Ma, S. Liu, Chaotic synchronization and anti-synchronization for a novel class of multiple chaotic systems via a sliding mode control scheme. Nonlinear Dyn, DoI 10.1007/s11071-011-0244-7 (2012). 1
- [28] H. Li Li,Y. L. Jiang,Z. L. Wang, Anti-synchronization and intermittent anti-synchronization of two identical hyperchaotic chua systems via impulsive control. Nonlinear Dyn. DoI 10.1007/s11071-014-1711-8 (2014). 1
- [29] M. M. Sawalla, M. S. M. Noorani, Adaptive reduced-order anti-synchronization of chaotic systems with fully unknown parameters. Commun Nonlinear Sci Numer Simulat 15, 3022-3034 (2010). 1
- [30] Li. Li. Fang, R. Li, Adaptive terminal sliding mode control for anti-synchronization of uncertain chaotic systems. Nonlinear Dyn. DoI 10.1007/s11071-013-1017-2 (2013). 1
- [31] O. I.Tacha,M.J. Pacheco. E. Serrano, I. N. Stouboulos, V. T.Pham, Determining the chaotic behavior in a fractional-order finance system with negative parameters. Nonlinear Dyn, 10.1007/s11071-018-4425-5 (2018). 1, 2
- [32] B. Xin, J. Zhang, Finite-time stabilitizing a fractional-order chaotic financial system with market confidence. Nonlinear Dyn, DoI 10.1007/s11071-014-1749-7 (2014). 1
- [33] A. Hajipour, H. Tavakoli, Analysis and circuit simulation of a novel nonlinear fractional incommensurate order financial system. Optic 127, 10643-10652 (2016). 1, 2
- [34] Z. H. Wang, X. Huang, Synchronization of a chaotic fractional order economical system with active control. Procedia Engineering 15, 516-520 (2011). 1
- [35] S. Dadras, H. R. Momeni, Control of a fractional-order economical system Via sliding mode. Physical A 389, 2434-2442 (2010). 1
- [36] A. Khan, A. Tyagi, Disturbance observer-based adaptive sliding mode hybrid projective synchronization of identical fractional-order financial system. Paramana- J. phys. DoI 10.1007/s12043-018-1555-8 (2018). 1
- [37] N. A. Camacho,D. Mermoud, J. A. Gallegos, Lyapunov functions for fractional order system. Common Nonlinear sci Numer simulate 19, 2951-2957 (2014). 1, 2.2
- [38] M. Ichise,Y. Nagayangi, T. Kojima, An analog simulation of noninteger order transfer functions for analysis of electrode process. J. Electroanal. Chem. 33, 253-265 (1971). 1
- [39] Zh. Wang, X. Huang, H. A. Shen, Control of an uncertain fractional-order economic system via adaptive sliding mode. Neurocomputing 83, 83-88 (2012). 1
- [40] N. Laskin, Fractional marcet dynamics. Phys. A 287, 482-492 (2000). 1
- [41] T.T. Hartley, C. F. Lorenzo, Dynamics and control of initialzed fractional-order systems. Nonlinear Dyn 29, 201-233 (2002). 1
- [42] R. Hifer, Applications of fractional calculus in physics. P. 472. Word scientific, Hackensack (2001). 1
- [43] R. C. Koeller, Application of fractional calculus to the theory of viscoelasticity. J. Appl. Mech 51, 299-307 (1984). 1
- [44] M. F. Danca,R. Garrappa, K.S. Wallace, G. Chen, Sustaining stable dynamics of a fractional-order chaotic financial system by parameter switching computers and mathematics with Applications. 66, 702-716(2013) 1
- [45] Zh. Zhang, J. Zhang, F. Cheng,F. Liu, A novel stability criterion of time-varying delay fractional-order financial systems based a new functional transformation Lemma. International Journal of Control, Automation and systems 17(X), 1-10 (2019). 1
- [46] M. Karimian, B. Naderi, Y. Edrisi Tabriz, Sensitivity analytic and synchronization of a new fractional-order financialsystem. Computational Methods for Differential Equations Vol. 9, No. 3, pp. 788-798 (2021). 1
Cite this article as:
- Malek Karimian, Encryption and Decryption of a Chaotic Fractional Order Financial System, Communications in Combinatorics, Cryptography & Computer Science, 2022(1), PP.23–33, 2022
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