International Journal of Mathematical, Engineering and Management Sciences

ISSN: 2455-7749

Asymptotic Stability Analysis Applied in Two and Three-Dimensional Discrete Systems to Control Chaos

Neha Kumra
Chitkara School of Engineering and Technology, Chitkara University, Baddi, Himachal Pradesh, India.

L. M. Saha
Institute for Innovation and Inventions with Mathematics and IT, Shiv Nadar University, Village Chithera, Tehsil Dadri, Gautambudh Nagar, Uttar Pradesh, India.

M. K. Das
Institute of Informatics & Communication, University of Delhi South Campus, Benito Juarez Road, New Delhi, India.

DOI https://doi.org/10.33889/IJMEMS.2021.6.2.042

Received on July 14, 2020
  ;
Accepted on January 27, 2021

Abstract

Asymptotic stability analysis applied to stabilize unstable fixed points and to control chaotic motions in two and three-dimensional discrete dynamical systems. A new set of parameter values obtained which stabilizes an unstable fixed point and control the chaotic evolution to regularity. The output of the considered model and that of the adjustable system continuously compared by a typical feedback and the difference used by the adaptation mechanism to modify the parameters. Suitable numerical simulation which are used thoroughly discussed and parameter values are adjusted. The findings are significant and interesting. This strategy has some advantages over many other chaos control methods in discrete systems but, however it can be applied within some limitations.

Keywords- Asymptotic stability, Control parameter, Chaos, Lyapunov exponents.

Citation

Kumra, N., Saha, L. M., & Das, M. K. (2021). Asymptotic Stability Analysis Applied in Two and Three-Dimensional Discrete Systems to Control Chaos. International Journal of Mathematical, Engineering and Management Sciences, 6(2), 677-687. https://doi.org/10.33889/IJMEMS.2021.6.2.042.

Conflict of Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

We are sincerely thankful to Chitkara University, Himachal Pradesh to provide congenial environment to carry out this work.

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