一个离散的猎物-掠食者模型的复杂动态,复杂的网络和随机建模,包含一个依赖比率的Ivlev功能响应
Md Mutakabbir Khan1, Md Jasim Uddin1, Dewan Fahim1
1Department of Mathematics, University of Dhaka, Dhaka 1000, Bangladesh.
这项研究探讨了离散的捕食者-猎物模型与比例依赖的伊夫勒夫反应,揭示了周期翻倍和尼马克-萨克分叉. 混沌管理技术应用于稳定这些复杂的动态.
科学领域:
- 数学生物学 数学生物学
- 动态系统理论 动态系统理论
- 生态生态学 生态生态学
背景情况:
- 捕食者-猎物模型在生态学中对于理解人口动态至关重要.
- 离散时间模型为人口波动和复杂行为提供了洞察力.
- 比例依赖的功能反应和Ivlev类型的相互作用对于现实的生态建模至关重要.
研究的目的:
- 分析捕食者-猎物模型的离散时间动态,其依赖比率的Ivlev功能响应.
- 在模型中调查分叉的发生和特征 (周期翻倍,尼马克-萨克).
- 在模型中探索混乱控制和管理策略,包括合网络场景和环境不确定性.
主要方法:
- 使用分叉理论和中心多样数定理进行代数分析.
- 数字模拟,包括相位肖像,轨道分析和莱普诺夫指数计算.
- 应用混乱控制技术 (状态反,奥特-格雷博吉-约克) 和随机模拟 (欧勒-马鲁雅马方法).
主要成果:
- 该模型在正相空间中表现出周期翻倍和尼马克-萨克二叉.
- 数字模拟证实了混乱现象,例如周期-11轨道和有吸引力的混乱集合.
- 混沌控制方法成功地稳定了混乱的轨迹;合网络在关键合时显示混乱的出现.
- 随机模拟揭示了环境不确定性下的系统行为.
结论:
- 离散的捕食者-猎物模型与依赖比率的伊夫勒夫反应显示了丰富的动态,包括分叉和混乱.
- 理论和数值发现是一致的,验证了稳定性和混乱过渡的分析.
- 混沌管理策略对于稳定系统是有效的,对理解复杂的生态网络和环境影响有影响.
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