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Volume 5, Issue 3
Dynamical Analysis for a General Jerky Equation with Random Excitation

Diandian Tang & Jingli Ren

DOI: 10.12150/jnma.2023.456

J. Nonl. Mod. Anal., 5 (2023), pp. 456-470.

Published online: 2023-08

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

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  • Abstract

A general jerky equation with random excitation is investigated in this paper. Before introducing the random excitation term, the equation is reduced to a two-dimensional model when undergoing a Hopf bifurcation. Then the model with the parametric excitation and external excitation is converted to a stochastic differential equation with singularity based on the stochastic average theory. For the equation, its dynamical behaviors are analyzed in different parameters' spaces, including the stability, stochastic bifurcation and stationary solution. Besides, numerical simulations are given to show the asymptotic behavior of the stationary solution.

  • Keywords

Jerky equation, stochastic stability, stochastic bifurcation, stationary solution.

  • AMS Subject Headings

34D20, 34F05, 34F10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JNMA-5-456, author = {Tang , Diandian and Ren , Jingli}, title = {Dynamical Analysis for a General Jerky Equation with Random Excitation}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2023}, volume = {5}, number = {3}, pages = {456--470}, abstract = {

A general jerky equation with random excitation is investigated in this paper. Before introducing the random excitation term, the equation is reduced to a two-dimensional model when undergoing a Hopf bifurcation. Then the model with the parametric excitation and external excitation is converted to a stochastic differential equation with singularity based on the stochastic average theory. For the equation, its dynamical behaviors are analyzed in different parameters' spaces, including the stability, stochastic bifurcation and stationary solution. Besides, numerical simulations are given to show the asymptotic behavior of the stationary solution.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2023.456}, url = {http://global-sci.org/intro/article_detail/jnma/21946.html} }
TY - JOUR T1 - Dynamical Analysis for a General Jerky Equation with Random Excitation AU - Tang , Diandian AU - Ren , Jingli JO - Journal of Nonlinear Modeling and Analysis VL - 3 SP - 456 EP - 470 PY - 2023 DA - 2023/08 SN - 5 DO - http://doi.org/10.12150/jnma.2023.456 UR - https://global-sci.org/intro/article_detail/jnma/21946.html KW - Jerky equation, stochastic stability, stochastic bifurcation, stationary solution. AB -

A general jerky equation with random excitation is investigated in this paper. Before introducing the random excitation term, the equation is reduced to a two-dimensional model when undergoing a Hopf bifurcation. Then the model with the parametric excitation and external excitation is converted to a stochastic differential equation with singularity based on the stochastic average theory. For the equation, its dynamical behaviors are analyzed in different parameters' spaces, including the stability, stochastic bifurcation and stationary solution. Besides, numerical simulations are given to show the asymptotic behavior of the stationary solution.

Diandian Tang & Jingli Ren. (2023). Dynamical Analysis for a General Jerky Equation with Random Excitation. Journal of Nonlinear Modeling and Analysis. 5 (3). 456-470. doi:10.12150/jnma.2023.456
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