一類(lèi)具有交叉反應(yīng)擴(kuò)散的捕食-食餌模型的動(dòng)態(tài)分歧

打開(kāi)文本圖片集

摘要：考慮一類(lèi)具有Holling-Ⅱ型功能反應(yīng)函數(shù)的交叉反應(yīng)擴(kuò)散模型在非齊次Dirichlet邊界條件下的動(dòng)態(tài)分歧問(wèn)題。首先，用譜分析理論得到對(duì)應(yīng)的線性化問(wèn)題特征值的臨界穿越條件；其次，選取環(huán)境承載系數(shù)為分歧參數(shù)，利用中心流形約化和動(dòng)態(tài)分歧理論得到該系統(tǒng)的動(dòng)態(tài)躍遷類(lèi)型和分歧解的解析表達(dá)式，最后，利用有限差分法，在不同的參數(shù)情形下給出系統(tǒng)的斑圖變化模式.

關(guān)鍵詞：反應(yīng)擴(kuò)散模型；特征值分析；動(dòng)態(tài)躍遷；數(shù)值模擬

中圖分類(lèi)號(hào)：O175.29文獻(xiàn)標(biāo)志碼：A文章編號(hào)：1671-5489（2024）05-1063-09

Dynamic Bifurcation of a Class of Predator-Prey Models with Cross Reaction Diffusion

QI Zicheng，LIURuikuan，WUChenlong

（School of Science，Southwest Petroleum University，Chengdu 610500，China）

Abstract：We considered the dynamic bifurcation problem of a class of cross-reaction-diffusion models with Holling-lI functional response function under non-homogeneous Dirichlet boundary conditions.Firstly，the critical crossing conditions for the corresponding linearization problem eigenvalues were obtained by using the spectral analysis theory.Secondly，the environmental carrying coefficient was selected as the bifurcation parameter，the analytical expression of the dynamic transition type and bifurcation solution of the system was obtained by using the center manifold reduction and the dynamic bifurcation theory.Finally，by using the finite difference method，the pattern change patterns of the system were given under different parameter conditions.

Keywords：reaction-diffusionmodel;eigenvalueanalysis;dynamictransition;numerical simulation

0引言

考慮如下一類(lèi)具有Holling-Ⅱ型功能反應(yīng)函數(shù)且具有交叉擴(kuò)散效應(yīng)的模型：

其中ΩCR”為有界光滑區(qū)域，u和v分別表示食餌和捕食者的種群密度，K為環(huán)境承載能力，d，和d，是物種的擴(kuò)散系數(shù)，d2和d，是交叉擴(kuò)散系數(shù)，0為捕食者的死亡率，是Holling-11功能反應(yīng)函數(shù)（該函數(shù)能較準(zhǔn)確地反映真實(shí)世界中無(wú)脊椎動(dòng)物與其捕食者之間的生物學(xué)相互作用），m表示相互作用對(duì)兩種物種相對(duì)影響的強(qiáng)度，u，>0和n>0為初值，u=0和。（剩余8930字）