Multistability and Instability of Competitive Neural Networks with Mexican-Hat-Type Activation Functions
We investigate the existence and dynamical behaviors of multiple equilibria for competitive neural networks with a class of general Mexican-hat-type activation functions. The Mexican-hat-type activation functions are not monotonously increasing, and the structure of neural networks with Mexican-hat-...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/901519 |
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| _version_ | 1832559177790128128 |
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| author | Xiaobing Nie Jinde Cao Shumin Fei |
| author_facet | Xiaobing Nie Jinde Cao Shumin Fei |
| author_sort | Xiaobing Nie |
| collection | DOAJ |
| description | We investigate the existence and dynamical behaviors of multiple equilibria
for competitive neural networks with a class of general Mexican-hat-type activation
functions. The Mexican-hat-type activation functions are not monotonously increasing, and the
structure of neural networks with Mexican-hat-type activation functions is totally different from
those with sigmoidal activation functions or nondecreasing saturated activation functions, which
have been employed extensively in previous multistability papers. By tracking the dynamics of
each state component and applying fixed point theorem and analysis method, some sufficient conditions
are presented to study the multistability and instability, including the total number of
equilibria, their locations, and local stability and instability. The obtained results extend and improve
the very recent works. Two illustrative examples with their simulations are given to verify
the theoretical analysis. |
| format | Article |
| id | doaj-art-e5a4525f04e84a5fb1f5118bcda9075a |
| 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-e5a4525f04e84a5fb1f5118bcda9075a2025-02-03T01:30:47ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/901519901519Multistability and Instability of Competitive Neural Networks with Mexican-Hat-Type Activation FunctionsXiaobing Nie0Jinde Cao1Shumin Fei2Department of Mathematics, and Research Center for Complex Systems and Network Sciences, Southeast University, Nanjing 210096, ChinaDepartment of Mathematics, and Research Center for Complex Systems and Network Sciences, Southeast University, Nanjing 210096, ChinaSchool of Automation, Southeast University, Nanjing 210096, ChinaWe investigate the existence and dynamical behaviors of multiple equilibria for competitive neural networks with a class of general Mexican-hat-type activation functions. The Mexican-hat-type activation functions are not monotonously increasing, and the structure of neural networks with Mexican-hat-type activation functions is totally different from those with sigmoidal activation functions or nondecreasing saturated activation functions, which have been employed extensively in previous multistability papers. By tracking the dynamics of each state component and applying fixed point theorem and analysis method, some sufficient conditions are presented to study the multistability and instability, including the total number of equilibria, their locations, and local stability and instability. The obtained results extend and improve the very recent works. Two illustrative examples with their simulations are given to verify the theoretical analysis.http://dx.doi.org/10.1155/2014/901519 |
| spellingShingle | Xiaobing Nie Jinde Cao Shumin Fei Multistability and Instability of Competitive Neural Networks with Mexican-Hat-Type Activation Functions Abstract and Applied Analysis |
| title | Multistability and Instability of Competitive Neural Networks with Mexican-Hat-Type Activation Functions |
| title_full | Multistability and Instability of Competitive Neural Networks with Mexican-Hat-Type Activation Functions |
| title_fullStr | Multistability and Instability of Competitive Neural Networks with Mexican-Hat-Type Activation Functions |
| title_full_unstemmed | Multistability and Instability of Competitive Neural Networks with Mexican-Hat-Type Activation Functions |
| title_short | Multistability and Instability of Competitive Neural Networks with Mexican-Hat-Type Activation Functions |
| title_sort | multistability and instability of competitive neural networks with mexican hat type activation functions |
| url | http://dx.doi.org/10.1155/2014/901519 |
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