Investigation of chaos behavior and integral sliding mode control on financial risk model

Sukono; Siti Hadiaty Yuningsih; Endang Rusyaman; Sundarapandian Vaidyanathan; Aceng Sambas; Sukono; Siti Hadiaty Yuningsih; Endang Rusyaman; Sundarapandian Vaidyanathan; Aceng Sambas

doi:10.3934/math.20221012

AIMS Mathematics

2022, Volume 7, Issue 10: 18377-18392. doi: 10.3934/math.20221012

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Research article Special Issues

Investigation of chaos behavior and integral sliding mode control on financial risk model

1.
Department of Mathematics, Universitas Padjadjaran, Jatinangor, Kabupaten Sumedang 45363, Indonesia
2.
Magister Program of Mathematics, Universitas Padjadjaran, Jatinangor, Kabupaten Sumedang 45363, Indonesia
3.
Centre for Control Systems, Vel Tech University, Avadi, Chennai-600062, Tamil Nadu, India
4.
Department of Mechanical Engineering, Universitas Muhammadiyah Tasikmalaya, 46196, Indonesia
5.
Institute of Strategic Industrial Decision Modelling (ISIDM), Universiti Utara Malaysia, Sintok, Kedah 06010, Malaysia

Received: 13 March 2022 Revised: 27 July 2022 Accepted: 01 August 2022 Published: 16 August 2022
MSC : 34H10, 34K18, 34K20, 37G15

This paper reports the finding of a new financial chaotic system. A new control law for completely synchronizing the new financial chaotic system with itself has been established using adaptive integral sliding mode control. We also find that the new financial chaotic system has fascinating traits including symmetry, equilibrium points, multistability, Lyapunov exponents and bifurcation diagrams. We illustrate all the main results of this research work using MATLAB phase plots. The Lyapunov characteristic exponents and analysis using bifurcation diagrams have resulted in a new financial chaos system showing chaos phenomena in the intervals of parameters 0 < a < 15, and parameters 0 < b < 0.25. The results of this study can be used to predict if there is chaos in financial risk. Chaotic systems have many applications in engineering like cryptosystems and secure communication systems.
- chaos,
- financial chaotic system,
- integral sliding mode control,
- synchronization
Citation: Sukono, Siti Hadiaty Yuningsih, Endang Rusyaman, Sundarapandian Vaidyanathan, Aceng Sambas. Investigation of chaos behavior and integral sliding mode control on financial risk model[J]. AIMS Mathematics, 2022, 7(10): 18377-18392. doi: 10.3934/math.20221012

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Abstract

This paper reports the finding of a new financial chaotic system. A new control law for completely synchronizing the new financial chaotic system with itself has been established using adaptive integral sliding mode control. We also find that the new financial chaotic system has fascinating traits including symmetry, equilibrium points, multistability, Lyapunov exponents and bifurcation diagrams. We illustrate all the main results of this research work using MATLAB phase plots. The Lyapunov characteristic exponents and analysis using bifurcation diagrams have resulted in a new financial chaos system showing chaos phenomena in the intervals of parameters 0 < a < 15, and parameters 0 < b < 0.25. The results of this study can be used to predict if there is chaos in financial risk. Chaotic systems have many applications in engineering like cryptosystems and secure communication systems.

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