On Offset Boosting in Chaotic System

Year 2021, Volume: 3 Issue: 2, 47 - 54, 30.11.2021

Chunbiao Li , Yicheng Jiang Xu Ma

https://doi.org/10.51537/chaos.959841

Cited By: 25

Abstract

Offset boosting is an important issue for chaos control due to its broadband property and polarity
control. There are two main approaches to realize offset boosting. One is resort to parameter introducing
where an offset booster realizes attractor boosting. The other one is by the means of periodic function or
absolute value function where a specific initial condition can extract out any self-reproduced or doubled
attractor with different offset. The former also provides a unique window for observing multistability and the
latter gives the direction for constructing desired multistability.

Keywords

Offset boosting, Chaos control, Multistability

References

• Akgul, A., C. Arslan, and B. Aricioglu, 2019 Image authentication using chaotic mixing systems. Chaos theory and applications 1: 1–18.
• Akgul, A., H. Calgan, I. Koyuncu, I. Pehlivan, and A. Istanbullu, 2016 Chaos-basedengineering applications with a 3D chaotic system without equilibrium points. Nonlinear Dynamics 84: 481–495.
• Bao, H., W. Liu, J. Ma, and H. Wu, 2020 Memristor initial-offset boosting in memristive hr neuron model with hidden firing patterns. International Journal of Bifurcation and Chaos 30: 2030029.
• C. Sprott, J., 2010 Elegant chaos: algebraically simple chaotic flows. World Scientific p. 304.
• C. Sprott, J. and A. Xiong, 2015 Classifying and quantifying basins of attraction. Chaos 25: 2230.
• Chen, M., X. Ren, H. Wu, Q. Xu, and B. Bao, 2019 Periodically varied initial offset boosting behaviors in a memristive system with cosine memductance. Frontiers of Information Technology and Electronic Engineering 20: 1706–1716.
• Chen, M., X. Ren, H. Wu, Q. Xu, and B. Bao, 2020 Interpreting initial offset boosting via reconstitution in integral domain. Chaos, Solitons and Fractals 131: 109544.
• Ding, D., X. Shan, J. Luo, Y. Hu, and L. Ding, 2020 Initial boosting phenomenon of a fractional-order hyperchaotic system based on dual memristors. Modern Physics Letters B 34: 2050191.
• Falco, A. D., T. F. Krauss, and A. Fratalocchi, 2012 Lifetime statistics of quantum chaos studied by a multiscale analysis. Applied Physics Letters 100: 1914–1917.
• Gu, S., S. He, H. Wang, and B. Du, 2021 Analysis of three types of initial offset-boosting behavior for a new fractional-order dynamical system. Chaos Solitons and Fractals 143: 110613.
• Kengne, J., G. Leutcho, and A. Telem, 2018 Reversals of period doubling, coexisting multiple attractors, and offset boosting in a novel memristive diode bridge-based hyperjerk circuit. Analog Integrated Circuits and Signal Processing 101: 379–399.
• Kingni, S. T., K. Rajagopal, S. Cicek, A. Srinivasan, and Karthikeyan, 2020 Dynamic analysis, FPGA implementation, and cryptographic application of an autonomous 5d chaotic system with offset boosting. Frontiers of Information Technology amd Electronic Engineering 21: 950–961.
• Li, C., G. Chen, J. Kurths, T. Lei, and Z. Liu, 2020a Dynamic transport: from bifurcation to multistability. Communications in Nonlinear Science and Numerical Simulation 95: 105600.
• Li, C., Z. Gu, Z. Liu, S. Jafari, and T. Kapitaniak, 2021 Constructing chaotic repellors. Chaos Solitons and Fractals 142: 110544.
• Li, C., T. Lei, X. Wang, and G. Chen, 2020b Dynamics editing based on offset boosting. Chaos 30: 063124.
• Li, C., T. Lu, G. Chen, and H. Xing, 2019 Doubling the coexisting attractors. Chaos 29: 051102.
• Li, C. and J. C. Sprott, 2016 Variable-boostable chaotic flows. International Journal for Light and Electron Optics 127: 10389–10398.
• Li, C. and J. C. Sprott, 2017 How to bridge attractors and repellors. International Journal of Bifurcation and Chaos 27: 1750149.
• Li, C., J. C. Sprott, W. Hu, and Y. Xu, 2017a Infinite multistability in a self-reproducing chaotic system. International Journal of Bifurcation and Chaos 27: 1750160.
• Li, C., J. Sun, J. C. Sprott, and T. Lei, 2020c Hidden attractors with conditional symmetry. International Journal of Bifurcation and Chaos 30: 2030042.
• Li, C., W. Xiong, and G. Chen, 2017b Diagnosing multistability by offset boosting. Nonlinear Dynamics 90: 1335–1341.
• Liu, J., G. Chen, and X. Zhao, 2020 Generalized synchronization and parameters identification of different-dimensional chaotic systems in the complex field. Fractals 29: 2150081–1–13.
• Lu, T., C. Li, S. Jafari, and F. Min, 2019 Controlling coexisting attractors of conditional symmetry. International Journal of Bifurcation and Chaos 29: 1950207.
• Lu, T., C. Li, X. Wang, C. Tao, and Z. Liu, 2020 A memristive chaotic system with offset-boostable conditional symmetry. The European Physical Journal Special Topics 229: 1059–1069.
• Ma, C., J. Mou, L. Xiong, S. Banerjee, and X. Han, 2021 Dynamical analysis of a new chaotic system: asymmetric multistability, offset boosting control and circuit realization. Nonlinear Dynamics 103: 1–14.
• Mezatio, B. A., M. T. Motchongom, B. W. Tekam, R. Kengne, R. Tchitnga, et al., 2019 A novel memristive 6d hyperchaotic autonomous system with hidden extreme multistability. Chaos Solitons and Fractals 120: 100–115.
• Wang, S., C. Wang, and C. Xu, 2020 An image encryption algorithm based on a hidden attractor chaos system and the knuth–durstenfeld algorithm. Optics and Lasers in Engineering 128: 105995.
• Wu, H., Y. Ye, B. Bao, M. Chen, and Q. Xu, 2019a Memristor initial boosting behaviors in a two-memristor-based hyperchaotic system. Chaos Solitons and Fractals 121: 178–185.
• Wu, H., Y. Ye, M. Chen, Q. Xu, and B. Bao, 2019b Periodically switched memristor initial boosting behaviors in memristive hypogenetic jerk system. IEEE Access 7: 1–1.
• Yuan, F., Y. Deng, Y. Li, and G. Wang, 2019 The amplitude, frequency and parameter space boosting in a memristor–meminductor-based circuit. Nonlinear Dynamics 96: 389–405.
• Zhang, S., Y. Zeng, Z. Li, and C. Zhou, 2018 Hidden extreme multistability, antimonotonicity and offset boosting control in a novel fractional-order hyperchaotic system without equilibrium. International Journal of Bifurcation and Chaos 28: 1850167.
• Zhang, S., J. Zheng, X. Wang, Z. Zeng, and S. He, 2020 Initial offset boosting coexisting attractors in memristive multi-double-scroll hopfield neural network. Nonlinear Dynamics 102: 2821–2841.
• Zhao, X., J. Liu, J. Mou, C. Ma, and F. Yang, 2020 Characteristics of a laser system in complex field and its complex selfsynchronization. The European Physical Journal Plus 135: 1–17.