Predicting solutions of the Lotka‐Volterra equation using hybrid deep network
Prediction of Lotka-Volterra equations has always been a complex problem due to their dynamic properties. In this paper, we present an algorithm for predicting the Lotka-Volterra equation and investigate the prediction for both the original system and the system driven by noise. This demonstrates th...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2022-11-01
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| Series: | Theoretical and Applied Mechanics Letters |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2095034922000642 |
| _version_ | 1797979858272256000 |
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| author | Zi-Fei Lin Yan-Ming Liang Jia-Li Zhao Jiao-Rui Li |
| author_facet | Zi-Fei Lin Yan-Ming Liang Jia-Li Zhao Jiao-Rui Li |
| author_sort | Zi-Fei Lin |
| collection | DOAJ |
| description | Prediction of Lotka-Volterra equations has always been a complex problem due to their dynamic properties. In this paper, we present an algorithm for predicting the Lotka-Volterra equation and investigate the prediction for both the original system and the system driven by noise. This demonstrates that deep learning can be applied in dynamics of population. This is the first study that uses deep learning algorithms to predict Lotka-Volterra equations. Several numerical examples are presented to illustrate the performances of the proposed algorithm, including Predator nonlinear breeding and prey competition systems, one prey and two predator competition systems, and their respective systems. All the results suggest that the proposed algorithm is feasible and effective for predicting Lotka-Volterra equations. Furthermore, the influence of the optimizer on the algorithm is discussed in detail. These results indicate that the performance of the machine learning technique can be improved by constructing the neural networks appropriately. |
| first_indexed | 2024-04-11T05:45:22Z |
| format | Article |
| id | doaj.art-25cd8ac9d27a4205a5f5adc7e229b688 |
| institution | Directory Open Access Journal |
| issn | 2095-0349 |
| language | English |
| last_indexed | 2024-04-11T05:45:22Z |
| publishDate | 2022-11-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Theoretical and Applied Mechanics Letters |
| spelling | doaj.art-25cd8ac9d27a4205a5f5adc7e229b6882022-12-22T04:42:15ZengElsevierTheoretical and Applied Mechanics Letters2095-03492022-11-01126100384Predicting solutions of the Lotka‐Volterra equation using hybrid deep networkZi-Fei Lin0Yan-Ming Liang1Jia-Li Zhao2Jiao-Rui Li3School of Statistics, Xi'an University of Finance and Economics, Xi'an 710100, China; China (Xi'an) Institute for Silk Road Research, Xi'an 710100, China; Corresponding author.School of Statistics, Xi'an University of Finance and Economics, Xi'an 710100, ChinaSchool of Statistics, Xi'an University of Finance and Economics, Xi'an 710100, ChinaChina (Xi'an) Institute for Silk Road Research, Xi'an 710100, ChinaPrediction of Lotka-Volterra equations has always been a complex problem due to their dynamic properties. In this paper, we present an algorithm for predicting the Lotka-Volterra equation and investigate the prediction for both the original system and the system driven by noise. This demonstrates that deep learning can be applied in dynamics of population. This is the first study that uses deep learning algorithms to predict Lotka-Volterra equations. Several numerical examples are presented to illustrate the performances of the proposed algorithm, including Predator nonlinear breeding and prey competition systems, one prey and two predator competition systems, and their respective systems. All the results suggest that the proposed algorithm is feasible and effective for predicting Lotka-Volterra equations. Furthermore, the influence of the optimizer on the algorithm is discussed in detail. These results indicate that the performance of the machine learning technique can be improved by constructing the neural networks appropriately.http://www.sciencedirect.com/science/article/pii/S2095034922000642Lotka-Volterra equationsHDN-LV algorithmStochastic Lotka-Volterra equationsParameter optimization |
| spellingShingle | Zi-Fei Lin Yan-Ming Liang Jia-Li Zhao Jiao-Rui Li Predicting solutions of the Lotka‐Volterra equation using hybrid deep network Theoretical and Applied Mechanics Letters Lotka-Volterra equations HDN-LV algorithm Stochastic Lotka-Volterra equations Parameter optimization |
| title | Predicting solutions of the Lotka‐Volterra equation using hybrid deep network |
| title_full | Predicting solutions of the Lotka‐Volterra equation using hybrid deep network |
| title_fullStr | Predicting solutions of the Lotka‐Volterra equation using hybrid deep network |
| title_full_unstemmed | Predicting solutions of the Lotka‐Volterra equation using hybrid deep network |
| title_short | Predicting solutions of the Lotka‐Volterra equation using hybrid deep network |
| title_sort | predicting solutions of the lotka volterra equation using hybrid deep network |
| topic | Lotka-Volterra equations HDN-LV algorithm Stochastic Lotka-Volterra equations Parameter optimization |
| url | http://www.sciencedirect.com/science/article/pii/S2095034922000642 |
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