Stability and Hopf Bifurcation of a Stochastic Cournot Duopoly Game in a Blockchain Cloud Services Market Driven by Brownian Motion
The blockchain technology has been rapidly popularizing and gaining a quick mileage in many domains owing to its innate nature, so there must be several tremendous market opportunities and uncertainties for the blockchain cloud service. We propose a Cournot duopoly game in a blockchain cloud service...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
IEEE
2020-01-01
|
| Series: | IEEE Access |
| Subjects: | |
| Online Access: | https://ieeexplore.ieee.org/document/9016171/ |
| _version_ | 1818935266571714560 |
|---|---|
| author | Baogui Xin Yanying Wang |
| author_facet | Baogui Xin Yanying Wang |
| author_sort | Baogui Xin |
| collection | DOAJ |
| description | The blockchain technology has been rapidly popularizing and gaining a quick mileage in many domains owing to its innate nature, so there must be several tremendous market opportunities and uncertainties for the blockchain cloud service. We propose a Cournot duopoly game in a blockchain cloud services market for cyber-physical-social systems (CPSS). Introducing Brownian noise disturbance to the deterministic Cournot duopoly game, we construct a stochastic Cournot duopoly game in a blockchain cloud service market with uncertainty. We analyze the stochastic stability of the Cournot duopoly game by the Lyapunov exponent method, the Lyapunov function, and the singular boundary theory. Then we investigate the stochastic Hopf bifurcation of the Cournot duopoly game by the invariant measure theory. At last, we numerically validate these results by the probability density. These results of stability and Hopf bifurcation illustrate complex behaviors of the stochastic Cournot duopoly game in the blockchain cloud services market. |
| first_indexed | 2024-12-20T05:17:26Z |
| format | Article |
| id | doaj.art-f7a29ae330a64120b5a41ca43b0d0dd2 |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-12-20T05:17:26Z |
| publishDate | 2020-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-f7a29ae330a64120b5a41ca43b0d0dd22022-12-21T19:52:07ZengIEEEIEEE Access2169-35362020-01-018414324143810.1109/ACCESS.2020.29765019016171Stability and Hopf Bifurcation of a Stochastic Cournot Duopoly Game in a Blockchain Cloud Services Market Driven by Brownian MotionBaogui Xin0https://orcid.org/0000-0002-7739-4808Yanying Wang1https://orcid.org/0000-0002-7082-0413College of Economics and Management, Shandong University of Science and Technology, Qingdao, ChinaCollege of Economics and Management, Shandong University of Science and Technology, Qingdao, ChinaThe blockchain technology has been rapidly popularizing and gaining a quick mileage in many domains owing to its innate nature, so there must be several tremendous market opportunities and uncertainties for the blockchain cloud service. We propose a Cournot duopoly game in a blockchain cloud services market for cyber-physical-social systems (CPSS). Introducing Brownian noise disturbance to the deterministic Cournot duopoly game, we construct a stochastic Cournot duopoly game in a blockchain cloud service market with uncertainty. We analyze the stochastic stability of the Cournot duopoly game by the Lyapunov exponent method, the Lyapunov function, and the singular boundary theory. Then we investigate the stochastic Hopf bifurcation of the Cournot duopoly game by the invariant measure theory. At last, we numerically validate these results by the probability density. These results of stability and Hopf bifurcation illustrate complex behaviors of the stochastic Cournot duopoly game in the blockchain cloud services market.https://ieeexplore.ieee.org/document/9016171/Lyapunov stabilitybifurcationstochastic cournot duopoly gameproduct differentiation strategystochastic differential equations |
| spellingShingle | Baogui Xin Yanying Wang Stability and Hopf Bifurcation of a Stochastic Cournot Duopoly Game in a Blockchain Cloud Services Market Driven by Brownian Motion IEEE Access Lyapunov stability bifurcation stochastic cournot duopoly game product differentiation strategy stochastic differential equations |
| title | Stability and Hopf Bifurcation of a Stochastic Cournot Duopoly Game in a Blockchain Cloud Services Market Driven by Brownian Motion |
| title_full | Stability and Hopf Bifurcation of a Stochastic Cournot Duopoly Game in a Blockchain Cloud Services Market Driven by Brownian Motion |
| title_fullStr | Stability and Hopf Bifurcation of a Stochastic Cournot Duopoly Game in a Blockchain Cloud Services Market Driven by Brownian Motion |
| title_full_unstemmed | Stability and Hopf Bifurcation of a Stochastic Cournot Duopoly Game in a Blockchain Cloud Services Market Driven by Brownian Motion |
| title_short | Stability and Hopf Bifurcation of a Stochastic Cournot Duopoly Game in a Blockchain Cloud Services Market Driven by Brownian Motion |
| title_sort | stability and hopf bifurcation of a stochastic cournot duopoly game in a blockchain cloud services market driven by brownian motion |
| topic | Lyapunov stability bifurcation stochastic cournot duopoly game product differentiation strategy stochastic differential equations |
| url | https://ieeexplore.ieee.org/document/9016171/ |
| work_keys_str_mv | AT baoguixin stabilityandhopfbifurcationofastochasticcournotduopolygameinablockchaincloudservicesmarketdrivenbybrownianmotion AT yanyingwang stabilityandhopfbifurcationofastochasticcournotduopolygameinablockchaincloudservicesmarketdrivenbybrownianmotion |