一类单种群模型的定态解和数值计算结果

应用分歧理论讨论一类单种群模型的非负定态解，并对该解的稳定性进行了分析．进一步对空间变量为一维的情形考虑全局分歧性态．利用数值延拓方法进行了分歧点的计算和分歧解曲线的跟踪，给出分歧图形．得到与理论分析相吻合的结果．

The Steady-State Bifurcation of a Kind of Single Population Model and Numerical Computation

he steady-state bifurcation and its stability for a single population model with reactiondiffusion terms developed in biology are discussed. In particular, global bifurcation is treated for the case where the space variable is of one dimension, and numerical calculation has been made. The birth rate of the population is assumed to be a bifurcation parameter and nontrivial nonnegative steady-state solution bifurcated from the trivial steady-state solution has been obtained with the bifurcation theory. Such a solution is proved unstable. For a space variable of one dimension, the global bifurcation found at the main eigenvalue is discussed. The bifurcation points are calculated, the curve of the bifurcation solution is tracked and the bifurcation graph is depicted using the numerical continuation method. The results obtained are in agreement with those by theoretical analysis.