Stability in Mean of Partial Variables for Coupled Stochastic Reaction-Diffusion Systems on Networks: A Graph Approach
This paper is devoted to investigating stability in mean of partial variables for coupled stochastic reaction-diffusion systems on networks (CSRDSNs). By transforming the integral of the trajectory with respect to spatial variables as the solution of the stochastic ordinary differential equations (...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/597502 |
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| _version_ | 1832564476520431616 |
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| author | Yonggui Kao Hamid Reza Karimi |
| author_facet | Yonggui Kao Hamid Reza Karimi |
| author_sort | Yonggui Kao |
| collection | DOAJ |
| description | This paper is devoted to investigating stability
in mean of partial variables for coupled stochastic reaction-diffusion systems
on networks (CSRDSNs). By transforming the integral of the trajectory with respect to spatial variables as the solution of the stochastic ordinary differential
equations (SODE) and using Itô formula, we establish some novel stability principles for uniform stability in mean, asymptotic stability in mean, uniformly asymptotic stability in mean, and exponential stability in mean of partial variables for CSRDSNs. These stability principles have a close relation with the
topology property of the network. We also provide a systematic
method for constructing global Lyapunov function for these CSRDSNs
by using graph theory. The new method can help to analyze the dynamics
of complex networks. An example is presented to illustrate the effectiveness and
efficiency of the obtained results. |
| format | Article |
| id | doaj-art-5fc6dd2b5a1a469f88ade6cd7608dbde |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-5fc6dd2b5a1a469f88ade6cd7608dbde2025-02-03T01:10:59ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/597502597502Stability in Mean of Partial Variables for Coupled Stochastic Reaction-Diffusion Systems on Networks: A Graph ApproachYonggui Kao0Hamid Reza Karimi1Department of Mathematics, Harbin Institute of Technology, Weihai 264209, ChinaDepartment of Engineering, Faculty of Technology and Science, University of Agder, 4898 Grimstad, NorwayThis paper is devoted to investigating stability in mean of partial variables for coupled stochastic reaction-diffusion systems on networks (CSRDSNs). By transforming the integral of the trajectory with respect to spatial variables as the solution of the stochastic ordinary differential equations (SODE) and using Itô formula, we establish some novel stability principles for uniform stability in mean, asymptotic stability in mean, uniformly asymptotic stability in mean, and exponential stability in mean of partial variables for CSRDSNs. These stability principles have a close relation with the topology property of the network. We also provide a systematic method for constructing global Lyapunov function for these CSRDSNs by using graph theory. The new method can help to analyze the dynamics of complex networks. An example is presented to illustrate the effectiveness and efficiency of the obtained results.http://dx.doi.org/10.1155/2014/597502 |
| spellingShingle | Yonggui Kao Hamid Reza Karimi Stability in Mean of Partial Variables for Coupled Stochastic Reaction-Diffusion Systems on Networks: A Graph Approach Abstract and Applied Analysis |
| title | Stability in Mean of Partial Variables for Coupled Stochastic Reaction-Diffusion Systems on Networks: A Graph Approach |
| title_full | Stability in Mean of Partial Variables for Coupled Stochastic Reaction-Diffusion Systems on Networks: A Graph Approach |
| title_fullStr | Stability in Mean of Partial Variables for Coupled Stochastic Reaction-Diffusion Systems on Networks: A Graph Approach |
| title_full_unstemmed | Stability in Mean of Partial Variables for Coupled Stochastic Reaction-Diffusion Systems on Networks: A Graph Approach |
| title_short | Stability in Mean of Partial Variables for Coupled Stochastic Reaction-Diffusion Systems on Networks: A Graph Approach |
| title_sort | stability in mean of partial variables for coupled stochastic reaction diffusion systems on networks a graph approach |
| url | http://dx.doi.org/10.1155/2014/597502 |
| work_keys_str_mv | AT yongguikao stabilityinmeanofpartialvariablesforcoupledstochasticreactiondiffusionsystemsonnetworksagraphapproach AT hamidrezakarimi stabilityinmeanofpartialvariablesforcoupledstochasticreactiondiffusionsystemsonnetworksagraphapproach |