CAJ | 학술논문

本文研究了带有分段常数变量的单种群连续模型的稳定性和分支行为。首先，通过计算将连续模型转化为对应的差分模型，使用线性稳定性理论在三种情况下研究了差分模型在正平衡态处局部渐近稳定的充分条件。其次，将参数r作为分支参数，利用分支理论研究了差分模型在正平衡态处产生翻转分支的条件。最后，数值模拟验证了理论分析的正确性。
본문연구료대유분단상수변량적단충군련속모형적은정성화분지행위。수선，통과계산장련속모형전화위대응적차분모형，사용선성은정성이론재삼충정황하연구료차분모형재정평형태처국부점근은정적충분조건。기차，장삼수r작위분지삼수，이용분지이론연구료차분모형재정평형태처산생번전분지적조건。최후，수치모의험증료이론분석적정학성。
The stability and bifurcation behavior of a population model with piecewise con-stant arguments are investigated in this paper. The discrete model determining the dynamical behavior of corresponding differential model is achieved by calculation. Firstly, the sufficient conditions for the local asymptotic stability of the steady state are achieved in three aspects based on the linearized stability analysis. Secondly, by choosing the parameter r as the bifurcation parameter and using the bifurcation theory, we find that the discrete equation undergoes a flip bifurcation at an excep-tive value of the parameter r. Finally, numerical examples are carried out to justify the main results in this work.