CAJ | 학술논문

研究了一类食饵-捕食者模型在R6内的离散化及其动力学行为。首先，利用二阶龙格-库塔方法将一类食饵-捕食者模型离散化，得到一类新的离散奇异系统，然后运用微分代数系统理论与分支理论讨论了系统在平衡点处的局部稳定性与分支问题，证明了Neimark-Sacker分支的存在性，并且选取捕获努力研究了Neimark-Sacker分支及其方向，最后通过数值模拟证明了我们的结论。
연구료일류식이-포식자모형재R6내적리산화급기동역학행위。수선，이용이계룡격-고탑방법장일류식이-포식자모형리산화，득도일류신적리산기이계통，연후운용미분대수계통이론여분지이론토론료계통재평형점처적국부은정성여분지문제，증명료Neimark-Sacker분지적존재성，병차선취포획노력연구료Neimark-Sacker분지급기방향，최후통과수치모의증명료아문적결론。
This paper investigate the discretization and the dynamical behavior of a prey -predator model in R 6 , First, apply-ing the second order Runge -Kutta method, we obtain a new discrete system .Second, by using the differential -algebraic theory and bifurcation theory , the local stability and bifurcation of the proposed model around an interior equilibrium is dis -cussed, and prove the Neimark-Sacker bifurcation exist .Then we analysis the Neimark-Sacker bifurcation and its direction by choosing the harvesting effort as the bifurcation parameter .Finally, a numerical simulation is presented to illustrate the the-oretical results .