| Summary: | 碩士 === 淡江大學 === 數學學系碩士班 === 98 === 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.
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