Persistence and Global Stability for Nonautonomous Cooperative System with Diffusion and Time Delay

Abstract

Abstract: A non-autonomous cooperative model with diffusion and continuous time delay is studied, where all parameters are time-dependent. The system, which is compose of two patches, has two species: one can diffuse between two patches, but the other is confined to one patch and cannot diffuse. It is proved that the system is uniformly persistent under appropriate conditions. Furthermore, sufficient conditions are established for global stability of the system.

Key words: persistence, time delay, global asymptotic stability, diffusion

摘要： 考虑了含连续时滞的两种群扩散合作的系统，其中一个种群能在两个斑块中移动，另一个种群限制在一个斑块中不能移动，给出了该系统一致持久性和全局稳定性的充分性条件。

关键词: 一致持久性, 时滞, 全局稳定性, 扩散系统

CLC Number:

O175.12

CHEN Fengde. Persistence and Global Stability for Nonautonomous Cooperative System with Diffusion and Time Delay[J]. Acta Scientiarum Naturalium Universitatis Pekinensis.

陈凤德. 含时滞扩散合作系统的一致持久性和全局稳定性[J]. 北京大学学报（自然科学版）.

[1]	GAO Jian, TONG Xin, HE Canfei. Impact of Lead Market on Transition Towards New Energy Technology in Automobile Industry in China [J]. Acta Scientiarum Naturalium Universitatis Pekinensis, 2023, 59(4): 671-680.
[2]	ZHENG Yufan, CAI Xuhui, KANG Ling, ZHANG Hongsheng, SONG Yu. Study of the Influence of Wind Field Uncertainty in Atmospheric Diffusion Emergency Forecast [J]. Acta Scientiarum Naturalium Universitatis Pekinensis, 2019, 55(5): 878-886.
[3]	HE Qichao,CAI Xuhui,SONG Yu,HU Min. Diagnostic Analysis of Atmospheric Transport and Diffusion Characteristics over the Pearl River Delta [J]. Acta Scientiarum Naturalium Universitatis Pekinensis, 2013, 49(6): 945-954.
[4]	MAO Xiyan,MENG Jijun,KANG Yufang. Natural Disasters Risk Assessment Based on Information Diffusion Model: Application and Improvement [J]. Acta Scientiarum Naturalium Universitatis Pekinensis, 2012, 48(3): 513-518.
[5]	KANG Ling,CAI Xuhui,WANG Zhiyuan,CHEN Jiayi,YAO Rentai. Numerical Analysis and Simulation of Characteristics of Atmospheric Diffusion in Coastal Area of Zhangzhou, Fujian [J]. Acta Scientiarum Naturalium Universitatis Pekinensis, 2011, 47(1): 71-78.
[6]	WEI Jie,SONG Yu,CAI Xuhui. High Resolution Simulations to Transport and Diffusion over Complex Terrain [J]. Acta Scientiarum Naturalium Universitatis Pekinensis, 2008, 44(6): 938-944.
[7]	YANG Lihong^{1, 4)}, LIU Fuchun²⁾, ZHANG Zhiqiang³⁾, HE Ping¹⁾, HAN Enhou²⁾, Qilu¹⁾ (¹⁾ New Energy Materials and Technology,Department of Applied Chemistry, College of Chemistr. Research on the Anti-Diffusion Behavior of ZnO/Polyurethane Coatings [J]. Acta Scientiarum Naturalium Universitatis Pekinensis, 2006, 42(7): 91-96.
[8]	XU Guiling,SITU Shangji. On Liang Qichao's Contribution to the Diffusion of Western Modern Geography in China [J]. Acta Scientiarum Naturalium Universitatis Pekinensis, 2006, 42(4): 510-514.
[9]	CHEN Yongchong,QI Lu,ZHANG Yonggang,CHEN Changqi. Phenomenological Theory of Interdiffusion Growth of Solid Phase [J]. Acta Scientiarum Naturalium Universitatis Pekinensis, 2006, 42(2): 168-174.
[10]	CUI Peng,ZHANG Li'ang,JI Lijiu,GAO Li. Comparisons of Two Smoothing Algorithms for Optimization in One-Dimensional Space [J]. Acta Scientiarum Naturalium Universitatis Pekinensis, 2003, 39(5): 681-689.
[11]	GUO Yu,CAI Xuhui,LIU Huizhi,CHEN Jiayi. Meso-scale Atmospheric Diffusion Patterns and Time Scales over Beijing Area [J]. Acta Scientiarum Naturalium Universitatis Pekinensis, 2002, 38(5): 705-712.
[12]	AN Yu,LI Genpei,RU Binggen. Crystallization and Preliminary X-ray Studies of Metallothionein-II from Rabbit Liver [J]. Acta Scientiarum Naturalium Universitatis Pekinensis, 2000, 36(2): 268-270.
[13]	TAN Wenchang,WU Wangyi,YAN Zongyi,WEN Gongbi. Diffusional Release of Drug from Polymeric Matrix: An Approximate Analytical Solution [J]. Acta Scientiarum Naturalium Universitatis Pekinensis, 1999, 35(5): 624-629.
[14]	HOU Shimin,ZENG Yan,XUE Zengquan,WU Quande. Effects of Charge Particles on The Fractal Structure [J]. Acta Scientiarum Naturalium Universitatis Pekinensis, 1999, 35(1): 107-111.
[15]	WU Junqiao,WANG Zhijun,WU Ke,ZHANG Jinlong,LI Chuanyi,YIN Daole. Postdeposition Resistance Relaxation of Semicontinuous Metal Films [J]. Acta Scientiarum Naturalium Universitatis Pekinensis, 1997, 33(3): 340-345.

Persistence and Global Stability for Nonautonomous Cooperative System with Diffusion and Time Delay

含时滞扩散合作系统的一致持久性和全局稳定性

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 15

Recommended Articles

Metrics