Identification of discrete chaotic maps with singular points
We investigate the ability of artificial neural networks to reconstruct discrete chaotic maps with singular points. We use as a simple test model the Cusp map. We compare the traditional Multilayer Perceptron, the Chebyshev Neural Network and the Wavelet Neural Network. The numerical scheme for the...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2001-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S1026022601000164 |
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| _version_ | 1832545799200833536 |
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| author | P. G. Akishin P. Akritas I. Antoniou V. V. Ivanov |
| author_facet | P. G. Akishin P. Akritas I. Antoniou V. V. Ivanov |
| author_sort | P. G. Akishin |
| collection | DOAJ |
| description | We investigate the ability of artificial neural networks to reconstruct discrete chaotic maps with singular points. We use as a simple test model the Cusp map. We compare the traditional Multilayer Perceptron, the Chebyshev Neural Network and the Wavelet Neural Network. The numerical scheme for the accurate determination of a singular point is also developed. We show that combining a neural network with the numerical algorithm for the determination of the singular point we are able to accurately approximate discrete chaotic maps with singularities. |
| format | Article |
| id | doaj-art-8e59d6fa9ff94072ab3f3d0ad15969cc |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2001-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-8e59d6fa9ff94072ab3f3d0ad15969cc2025-02-03T07:24:46ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2001-01-016314715610.1155/S1026022601000164Identification of discrete chaotic maps with singular pointsP. G. Akishin0P. Akritas1I. Antoniou2V. V. Ivanov3Laboratory of Computing Techniques and Automation, Joint Institute for Nuclear Research, Dubna 141980, Russialnternational Solvay Institute for Physics and Chemistry, CP-231, ULB, Campus Plaine, Bd. du Triomphe, Brussels 1050, Belgiumlnternational Solvay Institute for Physics and Chemistry, CP-231, ULB, Campus Plaine, Bd. du Triomphe, Brussels 1050, BelgiumLaboratory of Computing Techniques and Automation, Joint Institute for Nuclear Research, Dubna 141980, RussiaWe investigate the ability of artificial neural networks to reconstruct discrete chaotic maps with singular points. We use as a simple test model the Cusp map. We compare the traditional Multilayer Perceptron, the Chebyshev Neural Network and the Wavelet Neural Network. The numerical scheme for the accurate determination of a singular point is also developed. We show that combining a neural network with the numerical algorithm for the determination of the singular point we are able to accurately approximate discrete chaotic maps with singularities.http://dx.doi.org/10.1155/S1026022601000164Neural networks; Chaotic maps; Wavelets. |
| spellingShingle | P. G. Akishin P. Akritas I. Antoniou V. V. Ivanov Identification of discrete chaotic maps with singular points Discrete Dynamics in Nature and Society Neural networks; Chaotic maps; Wavelets. |
| title | Identification of discrete chaotic maps with singular points |
| title_full | Identification of discrete chaotic maps with singular points |
| title_fullStr | Identification of discrete chaotic maps with singular points |
| title_full_unstemmed | Identification of discrete chaotic maps with singular points |
| title_short | Identification of discrete chaotic maps with singular points |
| title_sort | identification of discrete chaotic maps with singular points |
| topic | Neural networks; Chaotic maps; Wavelets. |
| url | http://dx.doi.org/10.1155/S1026022601000164 |
| work_keys_str_mv | AT pgakishin identificationofdiscretechaoticmapswithsingularpoints AT pakritas identificationofdiscretechaoticmapswithsingularpoints AT iantoniou identificationofdiscretechaoticmapswithsingularpoints AT vvivanov identificationofdiscretechaoticmapswithsingularpoints |