一類基于比率的且具有收獲率和時(shí)滯的捕食系統(tǒng)的周期解

王暉

(內(nèi)蒙古民族大學(xué)數(shù)學(xué)學(xué)院,內(nèi)蒙古通遼 028000)

一類基于比率的且具有收獲率和時(shí)滯的捕食系統(tǒng)的周期解

王暉

(內(nèi)蒙古民族大學(xué)數(shù)學(xué)學(xué)院,內(nèi)蒙古通遼 028000)

研究一類基于比率且具有收獲和時(shí)滯的捕食系統(tǒng).證明了系統(tǒng)正周期解的存在性,并通過構(gòu)造適當(dāng)?shù)腖yapunov泛函,給出了正周期解全局穩(wěn)定的充分條件.

時(shí)滯;收獲率;比率依賴;周期解;Lyapunov泛函

DO I：10.3969/j.issn.1008-5513.2013.05.012

1 正周期解的存在性

生物種群的持續(xù)生存是數(shù)學(xué)生態(tài)學(xué)中捕食理論及其有關(guān)課題的一個(gè)重要方面.近年來,越來越多的生物學(xué)和生理學(xué)證據(jù)表明,在許多情形下,特別是當(dāng)捕食者不得不搜尋食物(因此不得不分享或競爭食物)時(shí),更切合實(shí)際且更一般的捕食-被捕食模型應(yīng)基于比率依賴?yán)碚?很多學(xué)者在這方面做出了貢獻(xiàn)[15].具有收獲率的系統(tǒng),由于存在開發(fā)項(xiàng),往往表現(xiàn)出復(fù)雜的動(dòng)力學(xué)行為.目前已有很多學(xué)者研究了此類模型[46].本文考慮了基于比率的HollingⅢ型功能反應(yīng)的且同時(shí)具有時(shí)滯和收獲率的捕食模型:

2 正周期解的唯一性及全局穩(wěn)定性

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The period ic solu tions of ratio-dependen t p redator-p rey m odel w ith harvesting and tim e delay

Wang Hui

(Mathematics College,Inner Mongolia University for the Nationalities,TongLiao 028000,China)

In this paper,we consider the Ratio-dependent predator-prey system w ith harvesting and time delay.The existence of positive period ic solu tion is proved,and by constructing app rop riate Lyapunov function, suf cient conditions are obtained to ensure the global stability of positive periodic solution.

time delay,harvesting,ratio-depedent,positive periodic solution,Lyapunov function

O175.13

A

1008-5513(2013)05-0520-09

2013-07-10.

王暉(1982-),碩士,講師,研究方向：生物數(shù)學(xué).

2010 MSC:34D 05