Abstract
A novel chaotic system of three-dimensional mathematic model is proposed in this paper. According to the changes of system parameters and initial values, the dynamical behaviors of the system are investigated in detail by using the classical dynamical analysis methods, such as Lyapunov exponents, bifurcation diagrams etc. Some abundant dynamical phenomena, such as chaos, transient chaos and period-doubling and so on are observed in numerical simulation by Matlab. The simulation results of Matlab can further prove the feasibility and flexibility of this system.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Leonova, G.A., Kuznetsov, N.V., Korzhemanovaa, N.A., Kusakina, D.V.: Lyapunov dimension formula for the global attractor of the Lorenz system. Commun. Nonlinear Sci. Numer. Simul. 41, 84–103 (2016)
Luo, R.Z., Zeng, Y.H.: The control and synchronization of fractional-order Genesio-tesi system. Nonlinear Dyn. 88, 1–11 (2017)
Sun, F.Y., Lü, Z.W.: Stability and spatial chaos in 2D Henon system. Appl. Math. Inf. Sci. 10, 739–746 (2016)
Fedele, G., Alfonso, L.D., Pin, G., Parisini, T.: Volterra’s kernels-based finite-time parameters estimation of the Chua system. IEEE Proc. 318, 121–130 (2018)
Molaie, M., Jafari, S., Sprott, J.C.: Simple chaotic flows stable equilibrium. Int. J. Bifurcat. Chaos 23, 1350188 (2013)
Zhou, L., Wang, C.H., Zhang, X., Yao, W.: Various attractors, coexisting attractors and antimonotonicity in a simple fourth-order memristive twin-t oscillator. Int. J. Bifurcat. Chaos 28, 1850050 (2018)
Bao, B.C., Xu, Q., Bao, H., Chen, M.: Extreme multistability in a memristive circuit. Electron. Lett. 52, 1008–1010 (2016)
Dudkowski, D., et al.: Hidden attractors in dynamical systems. Phys. Rep. 637, 1–50 (2016)
Bi, Q.S., Ma, R., Zhang, Z.D.: Bifurcation mechanism of the bursting oscillations in periodically excited dynamical system with two time scales. Nonlinear Dyn. 79, 101–110 (2015)
Ngonghala, C.N., Teboh-Ewungkem, M.I., Ngwa, G.A.: Observance of period-doubling bifurcation and chaos in an autonomous ODE model for malaria with vector demography. Theor. Ecol. 9, 1–15 (2016)
Din, Q., Khan, M.A.: Period-doubling bifurcation and chaos control in a discrete-time mosquito model. Comput. Ecol. Softw. 7, 153–166 (2017)
Nakagawa, S., Saito, T.: An RCOTA hysteresis chaos generator. IEEE Trans. Circ. Syst. I Fundam. Theor. Appl. 43, 1019–1021 (1996)
Sprott, J.C.: Simple chaotic systems and circuits. Am. J. Phys. 68, 758–763 (2000)
Ozoguz, S., Elwakil, A., Kennedy, M.P.: Experimental verification of the butterfly attractor in a modified Lorenz system. Inter. J. Bifurcat. Chaos 12, 1627–1632 (2002)
Elwakil, A., Kennedy, M.: Construction of classes of circuit-independent chaotic oscillators using passive-only nonlinear devices. IEEE Trans. Circ. Syst. I: Fundam. Theor. Appl. 48, 289–307 (2001)
Yu, S., Lü, J.H., Tang, W.K.S., Chen, G.: A general multi-scroll Lorenz system family and its realization via digital signal processors. Chaos 16, 033126 (2006)
Farajallah, M., Assad, S.E., Deforges, O.: Fast and secure chaos-based cryptosystem for images. Inter. J. Bifurcat. Chaos 26, 1650021-1–1650021-21 (2016)
Assad, S.E.: Chaos based information hiding and security. IEEE Internet Technol. Secur. Trans. Int. Conf. 7196, 67–72 (2016)
Noshadian, S., Ebrahimzade, A., Kazemitabar, S.J.: Optimizing chaos based image encryption. Multimed. Tools Appli. 1, 01–22 (2018)
Zhao, Y., University, A.: Research on text chaos classification technology based on improved SVM. Modern Electron. Tech. 39, 39–43 (2016)
Jafari, S., Pham, V.T., Moghtadaei, M., Kingni, S.T.: The relationship between chaotic maps and some chaotic systems with hidden attractors. Inter. J. Bifurcat. Chaos 26, 527–530 (2016)
Wang, Q.X., Yu, S.M., Li, C.Q., Lü, J.H., Fang, X.L., Guyeux, C.: Theoretical design and FPGA-based implementation of higher-dimensional digital chaotic systems. IEEE Trans. Circ. Syst. I Regul. Pap. 63, 401–412 (2016)
Li, C.B., Sprott, J.C., Xing, H.Y.: Constructing chaotic systems with conditional symmetry. Nonlinear Dyn. 87, 1351–1358 (2017)
Zhang, W.W., Ran-Chao, W.U.: Dual projective synchronization of fractional-order chaotic systems with a linear controller. Appl. Math. Mech. 37, 710–717 (2016)
Wang, Z.L., Ma, J., Cang, S.J., Wang, Z.H., Chen, Z.Q.: Simplified hyper-chaotic systems generating multi-wing non-equilibrium attractors. Optik Int. J. Light Electr. Opt. 127, 2424–2431 (2016)
Acknowledgments
The work is supported by the State Key Program of National Natural Science of China (Grant No. 61632002), the National Key R D Program of China for International S T Cooperation Projects (No. 2017YFE0103900), the National Natural Science of China (Grant Nos. 61603348, 61775198, 61603347, 61572446, 61472372), Science and Technology Innovation Talents Henan Province (Grant No. 174200510012), Research Program of Henan Province (Grant Nos. 172102210066, 17A120005, 182102210160), Youth Talent Lifting Project of Henan Province and the Science Foundation of for Doctorate Research of Zhengzhou University of Light Industry (Grant No. 2014BSJJ044).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Sun, J., Li, N., Wang, Y. (2018). Analysing Parameters Leading to Chaotic Dynamics in a Novel Chaotic System. In: Qiao, J., et al. Bio-inspired Computing: Theories and Applications. BIC-TA 2018. Communications in Computer and Information Science, vol 951. Springer, Singapore. https://doi.org/10.1007/978-981-13-2826-8_25
Download citation
DOI: https://doi.org/10.1007/978-981-13-2826-8_25
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-13-2825-1
Online ISBN: 978-981-13-2826-8
eBook Packages: Computer ScienceComputer Science (R0)