Non-explosion solutions for a class of stochastic physical diffusion oscillators
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866911859628572672 |
|---|---|
| author | Houas, Amrane Merahi, Fateh Moumni, Mustafa |
| author_facet | Houas, Amrane Merahi, Fateh Moumni, Mustafa |
| contents | In this work, we are interested in problems that are related to the physical phenomena of diffusion. We will focus on the theoretical aspect of the study, such as existence, uniqueness and non-explosive solutions. We will weaken the conditions imposed on the coefficients of the stochastic differential equations (SDE) that model some diffusion phenomena of mechanics. The work will be based on a general non-explosion criterion and we will obtain sufficient conditions so that the solution for a certain class of diffusions does not explode. We will construct Lyapunov functions that ensure the non-explosion of the solutions. Two important oscillators, namely the Duffing and the Van Der Pol oscillators, belong to this class. The Euler-Maruyama method is applied to these two oscillators to give us a simulation solution for them. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_19099 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-explosion solutions for a class of stochastic physical diffusion oscillators Houas, Amrane Merahi, Fateh Moumni, Mustafa Dynamical Systems Probability 60F99, 60G07, 37H05 In this work, we are interested in problems that are related to the physical phenomena of diffusion. We will focus on the theoretical aspect of the study, such as existence, uniqueness and non-explosive solutions. We will weaken the conditions imposed on the coefficients of the stochastic differential equations (SDE) that model some diffusion phenomena of mechanics. The work will be based on a general non-explosion criterion and we will obtain sufficient conditions so that the solution for a certain class of diffusions does not explode. We will construct Lyapunov functions that ensure the non-explosion of the solutions. Two important oscillators, namely the Duffing and the Van Der Pol oscillators, belong to this class. The Euler-Maruyama method is applied to these two oscillators to give us a simulation solution for them. |
| title | Non-explosion solutions for a class of stochastic physical diffusion oscillators |
| topic | Dynamical Systems Probability 60F99, 60G07, 37H05 |
| url | https://arxiv.org/abs/2404.19099 |