在短時間延遲的混合光的雙穩態系統中的不穩定與分歧

Abstract

在短時間延遲的混合光的雙穩態系統中,其數學模式為一延遲性方程式 dy(t)/dt=-y(t)+Asin^2[y(t-1)+1.2].我們將研究此方程式的不穩定與分 歧.數學分析與數值計算將被使用.在數學分析上,我們得到:在某些參數 下,會產生 Hopf bifurcation 和 Saddle node bifurcation, 而且有很 多參數是如此的.在數值計算上我們利用Spectral method 來解方程式並 求它的 Floquet multipliers ,並且利用 FFT (Fast Fourier Transformation ) 來看它的頻譜. The delay differential equation dy(t)/dt=-y(t)+Asin^2[y(t-1) +1.2] can be derived in hybrid optical bistable system with a short delay. We study the instability and bifurcation of the delay differential equation. Both mathematical analysis and numerical method are used. In mathematical analysis , Hopf bifurcation and Saddle node bifurcation points can obtain in some parameters.In numerical results, we apply spectral method to obtain the solution and Floquet multipliers. We can observe the solution in frequence domain by FFT (Fast Fourier Transformation ).