CAJ | 학술논문

研究了一类生态经济模型在R3＋内的离散化模型及其动力学行为。首先用庞克莱方法将一类微分代数捕食-食饵系统离散化,得到本文所研究的离散奇异系统。然后通过运用微分代数系统理论与分支理论讨论了模型的平衡点的局部稳定性和分支问题,证明了Neimark-Sacker分支的存在性,并选取捕捞行为的经济利益m作为分支参数,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果,并展现了模型的复杂的动力学行为。
연구료일류생태경제모형재R3＋내적리산화모형급기동역학행위。수선용방극래방법장일류미분대수포식-식이계통리산화,득도본문소연구적리산기이계통。연후통과운용미분대수계통이론여분지이론토론료모형적평형점적국부은정성화분지문제,증명료Neimark-Sacker분지적존재성,병선취포로행위적경제이익m작위분지삼수,연구료Neimark-Sacker분지급기방향;최후통과수치모의증명료아문적결과,병전현료모형적복잡적동역학행위。
In this paper,we analyze the discretization and the dynamical behaviors of a bioeconomic model in the closed first quadrant R3+.First,applying the Poincare scheme,we discrete the continuous-time predator-prey system and propose discrete singular system.By using the differential-algebraic system theory and bifurcation theory,local stability and bifurcation of the proposed model around interior equilibrium is discussed,and prove that Neimark-Sacker bifurcation exists.Then we analyze Neimark-Sacker bifurcation and its direction by choosing the economic interest m of harvesting as the parameter of the bifurcation.Finally,numerical simulations are presented not only to illustrate the theoretical results,but also to exhibit complex dynamical behavious of the model.