重庆师范大学学报（自然科学版）
重慶師範大學學報（自然科學版）
중경사범대학학보（자연과학판）
JOURNAL OF CHONGQING NORMAL UNIVERSITY（NATURAL SCIENCE EDITION）
2011年
3期
43-48
,共6页
食饵-捕食者模型%时滞%稳定性%Hopf分支%周期解
食餌-捕食者模型%時滯%穩定性%Hopf分支%週期解
식이-포식자모형%시체%은정성%Hopf분지%주기해
predator-prey model%time delay%stability%Hopf bifurcation%periodic solution
研究一类具有时滞和比率依赖型功能反应函数的食饵-捕食者模型的动力学行为,分析表明系统的渐近稳定关键依赖于时滞.通过选择时滞作为参数,分析了系统从正平衡点处产生极限环的Hopf分支问题,同时得到了系统正平衡点稳定的时滞范围为0＜τ＜τ+,给出数值模拟验证了作者所得结果的正确性.最后给出本文的主要结论:当τ∈[0,τ0)时,系统(2)的平衡点是渐近稳定的,当τ=τjk,k=1,2,3,4;j=0,1,2,…时,系统(2)在平衡点附近产生Hopf分支,时滞长度为τ+.
研究一類具有時滯和比率依賴型功能反應函數的食餌-捕食者模型的動力學行為,分析錶明繫統的漸近穩定關鍵依賴于時滯.通過選擇時滯作為參數,分析瞭繫統從正平衡點處產生極限環的Hopf分支問題,同時得到瞭繫統正平衡點穩定的時滯範圍為0＜τ＜τ+,給齣數值模擬驗證瞭作者所得結果的正確性.最後給齣本文的主要結論:噹τ∈[0,τ0)時,繫統(2)的平衡點是漸近穩定的,噹τ=τjk,k=1,2,3,4;j=0,1,2,…時,繫統(2)在平衡點附近產生Hopf分支,時滯長度為τ+.
연구일류구유시체화비솔의뢰형공능반응함수적식이-포식자모형적동역학행위,분석표명계통적점근은정관건의뢰우시체.통과선택시체작위삼수,분석료계통종정평형점처산생겁한배적Hopf분지문제,동시득도료계통정평형점은정적시체범위위0＜τ＜τ+,급출수치모의험증료작자소득결과적정학성.최후급출본문적주요결론:당τ∈[0,τ0)시,계통(2)적평형점시점근은정적,당τ=τjk,k=1,2,3,4;j=0,1,2,…시,계통(2)재평형점부근산생Hopf분지,시체장도위τ+.
In this paper, the dynamics of a delayed predator-prey model with ratio-dependent type functional response are considered. We show that the asymptotic behavior depends crucially on the time delay parameter. We are particularly interested in the study of the Hopf bifurcation problem to predict the occurrence of a limit cycle bifurcating from the positive equilibrium. By choosing the the delay as a bifurcation parameter, the length of delay which preserves the stability of the positive equilibrium is calculated( i. e. , 0 ＜τ＜τ+). Some numerical simulation for justifying the analytical findings is also provided. Main conclusions are as follows: the positive equilibrium of the system is asymptotically stable for τ∈[ 0,τo ). The syslay is τ+.
