中文摘要
電路控制導致渾沌在量子井雷射二極體上巳經由延遲反饋技術達成，經由外加延遲反饋控制項cSn(t-τ)，渾沌光線輸出可被發現。由分歧圖表得知准週期導致渾沌，此外，計算延遲微分方程李雅普諾夫指數的特殊演算法巳發展出來，此結果也驗証了此渾沌行為。

根據Pecora 和Carroll 的理論在兩個不同初始值的渾沌系統上造成同步，單向與雙向同步可皆由負的條件李雅普諾夫指數驗証，這是調節和解調的重要指標。

同步系統利用參數調整可使數位訊號經由渾沌光線傳輸，此外，其傳輸速率可由第一條件李雅普諾夫指數得知。

Electronic-controlled rounte to chaos in a quantum-well laser diode is carried out by a delayed-feedback technique. By introducing an extra delayed-feedback control term
cSn(t-τ),chaotic light output can be achieved. Bifurcation diagram suggests qusi-periodicity route to chaos. In addition, a practical algorithm to calculate the Lyapunov exponents for delay differential equations has been developed. The resulets from the Lyapunov exponents also indicates chaotic behaviors.

A synchronization scheme using quantum well laser diodes with delayed-feedback in optical chaotic communication is proposed. To synchronize between two identical chaotic system with different initial conditions, a drive and response system modelis constructed according to Pecora and Carroll's theory. Synthronization can be achieved for optical simplex and duplex transmissions provided that the conditional Lyopunov exponents for drive and response systems are all negative. This approach offers a key step toward the optical chaotic modulation and demodulation.

Optical chaotic transmission of a digital signal is investigated by the input parameter switch using the drive-response model according to Pecora and Carroll's theory. The digital message can in the receiving end. In addition, the first conditional Lyapunov exponent of the system is shown to be directly the transmission rate.

2 Chaos 5

2.1 Formulation ........................................5

2.2 Trajectory, Poincare map and Bifurcation diagram ....6

2.2.1 Trajectory ......................................6

2.2.2 Poincare map ....................................6

2.2.3 Bifurcation diagram .............................7

2.3 Lyapunov expinents ..................................8

3 Synchronization 11

3.1 Formulation .......................................11

3.2 Synchronization in simplex transmission ............11

3.3 Synchronization in duplex transmission .............13

4 Optical digital communication 14

5 Conclusion 17

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