Volume 1, Issue 4
Multiplicity and Stability of Equilibrium States of Three-Dimensional Nonlinear System

Suiming Shang & Yu Tian

J. Nonl. Mod. Anal., 1 (2019), pp. 595-604.

Published online: 2021-04

[An open-access article; the PDF is free to any online user.]

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  • Abstract

The multiplicity and stability of the equilibrium states of a three-dimensional differential system with initial conditions and three cross terms are studied in this paper. The existence and multiplicity of equilibrium states are given under the different qualifications of parameters. Besides, the local stability of the equilibrium state is shown by analyzing the eigenfunction of the Jacobi matrix. The global stability of the equilibrium state is obtained by constructing the Lyapunov function. Furthermore, the numerical simulation intuitively reflected the relationship of variables and verified the correctness of theoretical analysis.

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@Article{JNMA-1-595, author = {Shang , Suiming and Tian , Yu}, title = {Multiplicity and Stability of Equilibrium States of Three-Dimensional Nonlinear System}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2021}, volume = {1}, number = {4}, pages = {595--604}, abstract = {

The multiplicity and stability of the equilibrium states of a three-dimensional differential system with initial conditions and three cross terms are studied in this paper. The existence and multiplicity of equilibrium states are given under the different qualifications of parameters. Besides, the local stability of the equilibrium state is shown by analyzing the eigenfunction of the Jacobi matrix. The global stability of the equilibrium state is obtained by constructing the Lyapunov function. Furthermore, the numerical simulation intuitively reflected the relationship of variables and verified the correctness of theoretical analysis.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2019.595}, url = {http://global-sci.org/intro/article_detail/jnma/18842.html} }
TY - JOUR T1 - Multiplicity and Stability of Equilibrium States of Three-Dimensional Nonlinear System AU - Shang , Suiming AU - Tian , Yu JO - Journal of Nonlinear Modeling and Analysis VL - 4 SP - 595 EP - 604 PY - 2021 DA - 2021/04 SN - 1 DO - http://doi.org/10.12150/jnma.2019.595 UR - https://global-sci.org/intro/article_detail/jnma/18842.html KW - Equilibrium states, multiplicity, local stability, global stability, numerical simulation. AB -

The multiplicity and stability of the equilibrium states of a three-dimensional differential system with initial conditions and three cross terms are studied in this paper. The existence and multiplicity of equilibrium states are given under the different qualifications of parameters. Besides, the local stability of the equilibrium state is shown by analyzing the eigenfunction of the Jacobi matrix. The global stability of the equilibrium state is obtained by constructing the Lyapunov function. Furthermore, the numerical simulation intuitively reflected the relationship of variables and verified the correctness of theoretical analysis.

Suiming Shang & Yu Tian. (1970). Multiplicity and Stability of Equilibrium States of Three-Dimensional Nonlinear System. Journal of Nonlinear Modeling and Analysis. 1 (4). 595-604. doi:10.12150/jnma.2019.595
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