我們想要了解非線性電路中產生鉅形解的情況，經由微分方程式來看單一系統解的分析，探討解的穩定性以及是否有週期解產生。當輸入週期性外力會產生鉅形解。 接著我們想要了解兩個振盪系統，同時運作時所產生的現象及性質，我們考慮了Dirichlet邊界情況下耦合兩系統，經由電腦數值模擬計算，隨著耦合係數增加，看是否有同步化現象，發現耦合係數為30時，不同步且產生兩個極限環。因此我們再考慮Neumann的邊界情況下進行耦合，發現隨著耦合係數增加，會有同步化的現象。 In this study, we are interested in the existence of the spike solution of a nonlinear circuit. We will show the existence of a limit cycle with constant external force. Then, some examples were given to show the relation between the number of spike of a solution and the amplitude of the periodic external force. Also, we will study the coupling of two systems with two types of boundary conditions. With the Dirichlet boundary conditions, we found that the two systems almost synchronized when the coupling strength is large. However, the synchronization broke down when coupling strength is too big. We then observed that the number of the spike of the solution was increased when the coupling strength is increased. While with the Neumann boundary condition, the synchronization of the two systems were observed when the coupling strength is large enough. We do not see the change of the number of the spike of each solution when the coupling strength is different in this case.
