三种群捕食-食饵模型的分形特征与控制

数学物理学报 ›› 2019, Vol. 39 ›› Issue (4): 951-962.

三种群捕食-食饵模型的分形特征与控制

邵长旭,刘树堂*()

山东大学控制科学与工程学院济南 250061

收稿日期:2018-06-07 出版日期:2019-08-26 发布日期:2019-09-11
通讯作者: 刘树堂 E-mail:stliu618@163.com
基金资助:
国家自然科学基金重点项目(61533011)

Fractal Feature and Control of Three-Species Predator-Prey Model

Changxu Shao,Shutang Liu*()

School of Control Science and Engineering, Shandong University, Jinan 250061

Received:2018-06-07 Online:2019-08-26 Published:2019-09-11
Contact: Shutang Liu E-mail:stliu618@163.com
Supported by:
the Key Program of National Natural Science Foundation(61533011)

摘要/Abstract

摘要：

种群数量变化规律是动物生态学、资源管理学的核心问题之一，通过研究种群数量的变化，可以有效掌握种群动态、生活习性，这对于合理利用资源、保护生态有着重要的意义.该文从分形理论的角度讨论了三种群的捕食-食饵模型.研究了三维捕食-食饵模型的分形行为，通过研究Julia分形集的性质，探讨了使该模型趋于稳定的条件，并引入反馈控制项，实现了模型由不稳定向稳定的转换.此外，分析了单一种群数量变化对另外两个种群数量及生态系统的影响.最后，构造不同参数的非线性耦合项，将响应系统转变为目标系统，实现不同系统之间的同步.仿真证实了这些方法的有效性.

关键词: 捕食-食饵模型, 稳定, Julia集, 反馈控制, 同步

Abstract:

The law of population quantity change is one of the key problems in Animal Ecology and Resource Management. By studying the change of population quantity, we can effectively grasp the population dynamics and living habits, which is of great significance for the rational utilization of resources and the protection of ecology. In this paper, we discuss the three-species predator-prey model from the point of fractal theory. We construct the Julia set of 3D predatorprey model. By studying the property of Julia sets, we discuss the conditions for the model to be stable, and take feedback control terms to realize the transformation from instability to stability. In addition, the effects of single population changes on the other two populations and ecosystems were analyzed. Finally, the nonlinear coupling terms with different parameters are constructed, the response system is transformed into the target system, and the synchronization between different systems is realized. Simulation results show the effectiveness of the method.

Key words: Predator-prey model, Stability, Julia set, Feedback control, Synchronization

中图分类号:

邵长旭,刘树堂. 三种群捕食-食饵模型的分形特征与控制[J]. 数学物理学报, 2019, 39(4): 951-962.

Changxu Shao,Shutang Liu. Fractal Feature and Control of Three-Species Predator-Prey Model[J]. Acta mathematica scientia,Series A, 2019, 39(4): 951-962.

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