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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