Changing Dynamics of the First, Second and Third Approximations of the Exponential Chaotic System and Their Application in Secure Communication Using Synchronization

Broucke, M.: One parameter bifurcation diagram for Chua’s circuit. IEEE Trans. Circuits Syst. 34(2), 208–209 (1987) Chang, D., Li, Z., Wang, M., Zeng, Y.: A novel digital programmable multi-scroll chaotic system and its application in FPGA-based audio secure communication. AEU Int. J. Electron. Commun. 88, 20–29 (2018) Evans, D.J., Cohen, E., Searles, D.J., Bonetto, F.: Note on the Kaplan–Yorke dimension and linear transport coefficients. J. Stat. Phys. 101(1–2), 17–34 (2000) Feki, M.: An adaptive chaos synchronization scheme applied to secure communication. Chaos Solitons Fractals 18(1), 141–148 (2003) Geist, K., Parlitz, U., Lauterborn, W.: Comparison of different methods for computing Lyapunov exponents. Prog. Theor. Phys. 83(5), 875–893 (1990) Guo, W.: Lag synchronization of complex networks via pinning control. Nonlinear Anal. Real World Appl. 12(5), 2579–2585 (2011) Jafari, S., Pham, V.T., Kapitaniak, T.: Multiscroll chaotic sea obtained from a simple 3D system without equilibrium. Int. J. Bifurc. Chaos 26(02), 1650031 (2016) Jafari, S., Sprott, J.C., Molaie, M.: A simple chaotic OW with a plane of equilibria. Int. J. Bifurc. Chaos 26(06), 1650098 (2016) Jiang, C., Liu, S., Luo, C.: A new fractional-order chaotic complex system and its antisynchronization. In: Dr. Wong (ed) Abstract and Applied Analysis, vol. 2014. Hindawi, Cairo (2014) Jiang, C., Zhang, F., Li, T.: Synchronization and antisynchronization of n-coupled fractional-order complex chaotic systems with ring connection. Math. Methods Appl. Sci. 41(7), 2625–2638 (2018) Jimenez-Triana, A., Chen, G., Gauthier, A.: A parameter-perturbation method for chaos control to stabilizing UPOs. IEEE Trans. Circuits Syst. II Express Briefs 62(4), 407–411 (2015) Karavaev, A., Kulminskiy, D., Ponomarenko, V., Prokhorov, M.: An experimental communication scheme based on chaotic time-delay system with switched delay. Int. J. Bifurc. Chaos 25(10), 1550134 (2015) Khan, A., Trikha, P.: Study of earth’s changing polarity using compound difference synchronization. GEM-Int. J. Geomath. 11(1), 7 (2020) Khan, A., Trikha, P., Jahanzaib, L.S.: Dislocated hybrid synchronization via. tracking control and parameter estimation methods with application. Int. J. Model. Simul. 1–11 (2020) Khan, A., Jahanzaib, L.S., Trikha, P.: Analysis of a novel 3-D fractional order chaotic system. In: 2019 International Conference on Power Electronics, Control and Automation (ICPECA), pp. 1–6. IEEE (2019) Khan, A., Jahanzaib, L.S., Trikha, P.: Secure communication: using parallel synchronization technique on novel fractional order chaotic system. IFAC-PapersOnLine 53(7), 307–312 (2020) Khan, A., Jahanzaib, L.S., Trikha, P.: Fractional inverse matrix projective combination synchronization with application in secure communication. In: Proceedings of International Conference on Artificial Intelligence and Applications, pp. 93–101. Springer, Berlin (2020) Khan, A., Trikha, P.: Compound difference anti-synchronization between chaotic systems of integer and fractional order. SN Appl. Sci. 1, 757 (2019). https://doi.org/10.1007/s42452-019-0776-x Khan, A., Trikha, P., Jahanzaib, L.S.: Secure communication: using synchronization on a novel fractional order chaotic system. In: 2019 International Conference on Power Electronics, Control and Automation (ICPECA), pp. 1–5. IEEE (2019) Kousaka, T., Ueta, T., Kawakami, H.: Bifurcation of switched nonlinear dynamical systems. IEEE Trans. Circuits Syst. II Analog Digit. Signal Process. 46(7), 878–885 (1999) Li, C., Hu, W., Sprott, J.C., Wang, X.: Multistability in symmetric chaotic systems. Eur. Phys. J. Spec. Top. 224(8), 1493–1506 (2015) Li, C., Sprott, J.C.: Multistability in the Lorenz system: a broken butterfly. Int. J. Bifurc. Chaos 24(10), 1450131 (2014) Li, C., Sprott, J.C., Thio, W.: Linearization of the Lorenz system. Phys. Lett. A 379(10–11), 888–893 (2015) Lu, J., Chen, G., Cheng, D., Celikovsky, S.: Bridge the gap between the Lorenz system and the Chen system. Int. J. Bifurc. Chaos 12(12), 2917–2926 (2002) Luo, A.C.J.: A theory for synchronization of dynamical systems. Commun. Nonlinear Sci. Numer. Simul. 14(5), 1901–1951 (2009) Mahmoud, E.E., Jahanzaib, L.S., Trikha, P., Alkinani, M.H.: Anti-synchronized quad-compound combination among parallel systems of fractional chaotic system with application. Alex. Eng. J. (2020) Mahmoud, G.M., Mahmoud, E.E.: Phase and antiphase synchronization of two identical hyperchaotic complex nonlinear systems. Nonlinear Dyn. 61(1–2), 141–152 (2010) Mahmoud, G.M., Mahmoud, E.E.: Lag synchronization of hyperchaotic complex nonlinear systems. Nonlinear Dyn. 67(2), 1613–1622 (2012) Park, J.H.: Adaptive synchronization of hyperchaotic Chen system with uncertain parameters. Chaos Solitons Fractals 26(3), 959–964 (2005) Patra, P.K., Hoover, W.G., Hoover, C.G., Sprott, J.C.: The equivalence of dissipation from Gibbs entropy production with phase-volume loss in ergodic heat-conducting oscillators. Int. J. Bifurc. Chaos 26(05), 1650089 (2016) Pecora, L.M., Carroll, T.L.: Synchronization in chaotic systems. Phys. Rev. Lett. 64, 821–824 (1990). https://doi.org/10.1103/PhysRevLett.64.821 Pham, V.T., Jafari, S., Wang, X., Ma, J.: A chaotic system with different shapes of equilibria. Int. J. Bifurc. Chaos 26(04), 1650069 (2016) Qin, W.X., Chen, G.: On the boundedness of solutions of the Chen system. J. Math. Anal. Appl. 329(1), 445–451 (2007) Seyedzadeh, S.M., Mirzakuchaki, S.: A fast color image encryption algorithm based on coupled two-dimensional piecewise chaotic map. Signal Process. 92(5), 1202–1215 (2012) Tabor, M., Weiss, J.: Analytic structure of the Lorenz system. Phys. Rev. A 24(4), 2157 (1981) Trikha, P., Jahanzaib, L.S.: Dynamical analysis of a novel 5-D hyper-chaotic system with no equilibrium point and its application in secure communication. Differ. Geom. Dyn. Syst. 22, 269–288 (2020) Torrieri, D.J.: Principles of Secure Communication Systems. Artech House, INC, Norwood (1985) Trikha, P., Jahanzaib, L.S.: Secure communication: using double compound-combination hybrid synchronization. In: Proceedings of International Conference on Artificial Intelligence and Applications, pp. 81–91. Springer, Berlin (2020) Vaidyanathan, S., Volos, C.K., Kyprianidis, I., Stouboulos, I., Pham, T.: Analysis, adaptive control and anti-synchronization of a six-term novel jerk chaotic system with two exponential nonlinearities and its circuit simulation. J. Eng. Sci. Technol. Rev. 8(2) (2015) Wang, X., Teng, L., Qin, X.: A novel colour image encryption algorithm based on chaos. Signal Process. 92(4), 1101–1108 (2012) Wolf, A., Swift, J.B., Swinney, H.L., Vastano, J.A.: Determining Lyapunov exponents from a time series. Phys. D Nonlinear Phenom. 16(3), 285–317 (1985) Wu, Y., Noonan, J.P., Yang, G., Jin, H.: Image encryption using the two-dimensional logistic chaotic map. J. Electron. Imaging 21(1), 013014 (2012) Wu, Z., Zhang, X., Zhong, X.: Generalized chaos synchronization circuit simulation and asymmetric image encryption. IEEE Access 7, 37989–38008 (2019) Yu, W.: Passive equivalence of chaos in Lorenz system. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 46(7), 876–878 (1999) Zabihi, M., Kiranyaz, S., Rad, A.B., Katsaggelos, A.K., Gabbouj, M., Ince, T.: Analysis of high-dimensional phase space via Poincare section for patient-specific seizure detection. IEEE Trans. Neural Syst. Rehabil. Eng. 24(3), 386–398 (2016) Zhang, H., Liu, D., Wang, Z.: Controlling Chaos: Suppression, Synchronization and Chaotification. Springer, Berlin (2009) Zhang, X., Yu, S., Chen, P., Lü, J., He, J., Lin, Z.: Design and ARM-embedded implementation of a chaotic secure communication scheme based on H. 264 selective encryption. Nonlinear Dyn. 89(3), 1949–1965 (2017)