对于非线性猎物捕食者动态系统的古德尔曼尼神经网络程序.
Hafsa Alkaabi1, Noura Alkarbi1, Nouf Almemari1
1Department of Mathematical Sciences, College of Science, United Arab Emirates University, P. O. Box 15551, Al Ain, United Arab Emirates.
本研究引入了古德曼尼神经网络 (GNN) 与遗传算法和内部点算法 (GA-IPA) 结合在一起,以准确地建模非线性猎物捕食者动态. 新的GNNs-GA-IPA方法在生态模拟中显示出高精度和可靠性.
科学领域:
- 计算数学 计算数学 计算数学
- 生态建模 生态建模
- 人工智能的人工智能
背景情况:
- 非线性动态对于理解复杂的生态系统至关重要,比如猎物与掠食者的相互作用.
- 这些系统的准确建模需要强大的数值方法,能够处理复杂的关系和可变参数.
研究的目的:
- 设计和实施一个新的古德曼尼神经网络 (GNN) 框架,用于解决猎物捕食者系统 (NDPPS) 的非线性动态.
- 整合全球和本地搜索算法,特别是遗传算法 (GA) 和内部点算法 (IPA),以优化GNN模型 (GNNs-GA-IPA).
主要方法:
- 为NDPPS量身定制的Gudermannian神经网络 (GNNs) 的开发.
- 混合优化策略将基因算法 (GA) 和内部点算法 (IPA) 结合起来,用于GNN培训.
- 使用NDPPS和初始条件构建和优化基于错误的优点函数.
主要成果:
- 拟议的GNNs-GA-IPA有效地解决了六个具有可变系数的NDPPS病例.
- 通过GNN-GA-IPA结果和Runge-Kutta参考解决方案之间的密切一致来证明的高准确性.
- 在10-06到10-08的范围内实现了绝对误差,证实了模型的一致性和可靠性.
结论:
- GNNs-GA-IPA混合方法提供了一个非常准确和可靠的方法来模拟非线性猎物-掠食者动态.
- 统计分析 (最小,中位数,半四分位数范围) 验证了模型对捕食者和猎物种群的稳定性.
- 提出的方法为生态研究和动态系统分析提供了一个强大的工具.
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