Chaotic Phenomena, Sensitivity Analysis, Bifurcation Analysis, and New Abundant Solitary Wave Structures of The Two Nonlinear Dynamical Models in Industrial Optimization
Abstract
:1. Introduction
2. Exposition of the Mentioned Method
3. Application of the LWE
3.1. Chaotic Analysis of LWE
3.2. Sensitivity Analysis of LWE
- (i)
- and ;
- (ii)
- and ;
- (iii)
- and ;
- (iv)
- and
3.3. Bifurcation and Phase Portrait Analysis of LWE
- The equilibrium position denotes a saddle point, whereas ;
- The equilibrium position stands for a center point, whereas ;
- The equilibrium position characterizes a cuspid point, whereas .
3.4. Soliton Solutions of LWE
4. Application of the SNNVS
4.1. Chaotic Analysis of SNNVS
4.2. Sensitivity Analysis of SNNVS
- (i)
- and ;
- (ii)
- and ;
- (iii)
- and ;
- (iv)
- and
4.3. Bifurcation and Phase Portrait Analysis of SNNVS
- The equilibrium standpoint refer to a saddle point, while ;
- The equilibrium standpoint means a center point, while ;
- The equilibrium standpoint implies a cuspid point, while .
4.4. Soliton Solutions of SNNVS
5. Graphical Representation of Soliton Solutions
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Miah, M.M.; Alsharif, F.; Iqbal, M.A.; Borhan, J.R.M.; Kanan, M. Chaotic Phenomena, Sensitivity Analysis, Bifurcation Analysis, and New Abundant Solitary Wave Structures of The Two Nonlinear Dynamical Models in Industrial Optimization. Mathematics 2024, 12, 1959. https://doi.org/10.3390/math12131959
Miah MM, Alsharif F, Iqbal MA, Borhan JRM, Kanan M. Chaotic Phenomena, Sensitivity Analysis, Bifurcation Analysis, and New Abundant Solitary Wave Structures of The Two Nonlinear Dynamical Models in Industrial Optimization. Mathematics. 2024; 12(13):1959. https://doi.org/10.3390/math12131959
Chicago/Turabian StyleMiah, M. Mamun, Faisal Alsharif, Md. Ashik Iqbal, J. R. M. Borhan, and Mohammad Kanan. 2024. "Chaotic Phenomena, Sensitivity Analysis, Bifurcation Analysis, and New Abundant Solitary Wave Structures of The Two Nonlinear Dynamical Models in Industrial Optimization" Mathematics 12, no. 13: 1959. https://doi.org/10.3390/math12131959
APA StyleMiah, M. M., Alsharif, F., Iqbal, M. A., Borhan, J. R. M., & Kanan, M. (2024). Chaotic Phenomena, Sensitivity Analysis, Bifurcation Analysis, and New Abundant Solitary Wave Structures of The Two Nonlinear Dynamical Models in Industrial Optimization. Mathematics, 12(13), 1959. https://doi.org/10.3390/math12131959