Dynamics of the Exponential Population Growth System with Mixed Fractional Brownian Motion
This paper examines the dynamics of the exponential population growth system with mixed fractional Brownian motion. First, we establish some useful lemmas that provide powerful tools for studying the stochastic differential equations with mixed fractional Brownian motion. We offer some explicit expr...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2021-01-01
|
| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2021/5079147 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832547574106554368 |
|---|---|
| author | Weijun Ma Wei Liu Quanxin Zhu Kaibo Shi |
| author_facet | Weijun Ma Wei Liu Quanxin Zhu Kaibo Shi |
| author_sort | Weijun Ma |
| collection | DOAJ |
| description | This paper examines the dynamics of the exponential population growth system with mixed fractional Brownian motion. First, we establish some useful lemmas that provide powerful tools for studying the stochastic differential equations with mixed fractional Brownian motion. We offer some explicit expressions and numerical characteristics such as mathematical expectation and variance of the solutions of the exponential population growth system with mixed fractional Brownian motion. Second, we propose two sufficient and necessary conditions for the almost sure exponential stability and the kth moment exponential stability of the solution of the constant coefficient exponential population growth system with mixed fractional Brownian motion. Furthermore, we conduct some large deviation analysis of this mixed fractional population growth system. To the best of the authors’ knowledge, this is the first paper to investigate how the Hurst index affects the exponential stability and large deviations in the biological population system. It is interesting that the phenomenon of large deviations always occurs for addressed system when 1/2<H<1. Moreover, several numerical simulations are reported to show the effectiveness of the proposed approach. |
| format | Article |
| id | doaj-art-675a822a9b8f42618c81c02d8e9ab6b3 |
| institution | Kabale University |
| issn | 1099-0526 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-675a822a9b8f42618c81c02d8e9ab6b32025-02-03T06:44:15ZengWileyComplexity1099-05262021-01-01202110.1155/2021/5079147Dynamics of the Exponential Population Growth System with Mixed Fractional Brownian MotionWeijun Ma0Wei Liu1Quanxin Zhu2Kaibo Shi3School of Information EngineeringSchool of Mathematics and Information ScienceSchool of Mathematics and StatisticsSchool of Electronic Information and Electrical EngineeringThis paper examines the dynamics of the exponential population growth system with mixed fractional Brownian motion. First, we establish some useful lemmas that provide powerful tools for studying the stochastic differential equations with mixed fractional Brownian motion. We offer some explicit expressions and numerical characteristics such as mathematical expectation and variance of the solutions of the exponential population growth system with mixed fractional Brownian motion. Second, we propose two sufficient and necessary conditions for the almost sure exponential stability and the kth moment exponential stability of the solution of the constant coefficient exponential population growth system with mixed fractional Brownian motion. Furthermore, we conduct some large deviation analysis of this mixed fractional population growth system. To the best of the authors’ knowledge, this is the first paper to investigate how the Hurst index affects the exponential stability and large deviations in the biological population system. It is interesting that the phenomenon of large deviations always occurs for addressed system when 1/2<H<1. Moreover, several numerical simulations are reported to show the effectiveness of the proposed approach.http://dx.doi.org/10.1155/2021/5079147 |
| spellingShingle | Weijun Ma Wei Liu Quanxin Zhu Kaibo Shi Dynamics of the Exponential Population Growth System with Mixed Fractional Brownian Motion Complexity |
| title | Dynamics of the Exponential Population Growth System with Mixed Fractional Brownian Motion |
| title_full | Dynamics of the Exponential Population Growth System with Mixed Fractional Brownian Motion |
| title_fullStr | Dynamics of the Exponential Population Growth System with Mixed Fractional Brownian Motion |
| title_full_unstemmed | Dynamics of the Exponential Population Growth System with Mixed Fractional Brownian Motion |
| title_short | Dynamics of the Exponential Population Growth System with Mixed Fractional Brownian Motion |
| title_sort | dynamics of the exponential population growth system with mixed fractional brownian motion |
| url | http://dx.doi.org/10.1155/2021/5079147 |
| work_keys_str_mv | AT weijunma dynamicsoftheexponentialpopulationgrowthsystemwithmixedfractionalbrownianmotion AT weiliu dynamicsoftheexponentialpopulationgrowthsystemwithmixedfractionalbrownianmotion AT quanxinzhu dynamicsoftheexponentialpopulationgrowthsystemwithmixedfractionalbrownianmotion AT kaiboshi dynamicsoftheexponentialpopulationgrowthsystemwithmixedfractionalbrownianmotion |