Exponential Stability for an Opinion Formation Model with a Leader Associated with Fractional Differential Equations
This paper studies the dynamics of an opinion formation model with a leader associated with a system of fractional differential equations. We applied the concept of α-exponential stability and the uniqueness of equilibrium to show the consensus of the followers with the leader. A sufficient conditio...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2022/3973157 |
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| _version_ | 1832551194078216192 |
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| author | Dussadee Somjaiwang Parinya Sa Ngiamsunthorn |
| author_facet | Dussadee Somjaiwang Parinya Sa Ngiamsunthorn |
| author_sort | Dussadee Somjaiwang |
| collection | DOAJ |
| description | This paper studies the dynamics of an opinion formation model with a leader associated with a system of fractional differential equations. We applied the concept of α-exponential stability and the uniqueness of equilibrium to show the consensus of the followers with the leader. A sufficient condition for the consensus is obtained for both fractional formation models with and without time-dependent external inputs. Moreover, numerical results are provided to illustrate the dynamical behavior. |
| format | Article |
| id | doaj-art-75d789f9dd35449ea74d3ba08b43b5b4 |
| institution | Kabale University |
| issn | 1687-9651 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-75d789f9dd35449ea74d3ba08b43b5b42025-02-03T06:04:41ZengWileyInternational Journal of Differential Equations1687-96512022-01-01202210.1155/2022/3973157Exponential Stability for an Opinion Formation Model with a Leader Associated with Fractional Differential EquationsDussadee Somjaiwang0Parinya Sa Ngiamsunthorn1The Demonstration School of Kanchanaburi Rajabhat UniversityDepartment of MathematicsThis paper studies the dynamics of an opinion formation model with a leader associated with a system of fractional differential equations. We applied the concept of α-exponential stability and the uniqueness of equilibrium to show the consensus of the followers with the leader. A sufficient condition for the consensus is obtained for both fractional formation models with and without time-dependent external inputs. Moreover, numerical results are provided to illustrate the dynamical behavior.http://dx.doi.org/10.1155/2022/3973157 |
| spellingShingle | Dussadee Somjaiwang Parinya Sa Ngiamsunthorn Exponential Stability for an Opinion Formation Model with a Leader Associated with Fractional Differential Equations International Journal of Differential Equations |
| title | Exponential Stability for an Opinion Formation Model with a Leader Associated with Fractional Differential Equations |
| title_full | Exponential Stability for an Opinion Formation Model with a Leader Associated with Fractional Differential Equations |
| title_fullStr | Exponential Stability for an Opinion Formation Model with a Leader Associated with Fractional Differential Equations |
| title_full_unstemmed | Exponential Stability for an Opinion Formation Model with a Leader Associated with Fractional Differential Equations |
| title_short | Exponential Stability for an Opinion Formation Model with a Leader Associated with Fractional Differential Equations |
| title_sort | exponential stability for an opinion formation model with a leader associated with fractional differential equations |
| url | http://dx.doi.org/10.1155/2022/3973157 |
| work_keys_str_mv | AT dussadeesomjaiwang exponentialstabilityforanopinionformationmodelwithaleaderassociatedwithfractionaldifferentialequations AT parinyasangiamsunthorn exponentialstabilityforanopinionformationmodelwithaleaderassociatedwithfractionaldifferentialequations |