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 ...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.展开更多
基金supported by the National Natural Science Foundation of China(No.11902234)Natural Science Basic Research Program of Shaanxi(No.2020JQ-853)+2 种基金China(Xi’an)Silk Road Research Institute Scientific Research Project(No.2019ZD02)Shaanxi Provincial Department of Education Youth Innovation Team Scientific Research Project(No.22JP025)the Young Talents Development Support Program of Xi’an University of Finance and Economics。
文摘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.
