通常系統工程藉由供給（supply）與需求（demand）來描述許多事物之間的相互關係與交互作用，當供給與需求本身有了衝突，就產生了內部競爭（interspecific competition）與外部競爭（intraspecific competition），最後達成平衡。本文即運用生態學（ecology）學者的模型創造出非線性系統模型，並找出平衡點，分析其穩定度，並且對此平衡點加以討論。 本研究主要是探討非線性系統的特例，給予固定的參數值而找到極限環（limit cycle），為了使非線性系統收斂而易於控制，因此考慮了自比較項（self-competition term）與隨機干擾（white noises），最後導入福客爾-普朗克方程式（Fokker-Planck equation），得到變數的機率密度函數，並且討論其現象。 System engineering generally describes the correlation and reciprocation between lots of things by supply and demand. If there is a conflict on itself, the interspecific competition and the intraspecific competition would come into existence. And the system reach the balance in the end. In this article, we use scholar’s model in ecology to create the non-linear system model, finding out the equilibrium point, analyzing the stability, and discuss equilibrium point at the same time. The research is to discuss the special case in the non-linear system. We use the fixed parameter value to find out the limit cycle. In order to make the non-linear system convergent and easy to control, the self-competition term and white noises are being used. Finally, we can get probability density function of the variable and discuss the result by the Fokker-Planck equation.
