臺灣博碩士論文加值系統

我們研究在週期性外力驅動下兩種不同擁有自身韻律的模型，在第一部分使用三種不同波形(方波、餘弦波與三角波)驅動有噪音影響下的可激發FitzHugh Nagumo粒子，特定的耦合強度會有律動間隙(beat skipping)而產生多週期現象，從峰間距(inter spike interval)分佈圖中可量化各律動間隙週期所占的比例，此比例與系統回復有關。第二部分使用均勻轉子驅動相振子與相單元，在某些特定範圍的耦合強度會有鎖頻，在所有情況中，隨著耦合強度增加可以找到鎖頻中平均轉速比的極大值，而這些鎖頻比都會滿足m倍，m為整數，其間出現的鎖頻比是依序出現，重要的是在此系統鎖頻的極大值可以比驅動頻率還要大，有頻率增強的現象，從相軌跡來看都滿足鎖頻比值為M時，剛好是M倍週期。

We consider two nonlinear dynamical model(FitzHugh-Nagumo model and phase model) under periodic drive.
First,external forcing on excitable FitzHugh-Nagumo (FHN) element in the presence of noise and is investigated as a function of the coupling strength.Periodic forcing of triangle, cosine and square waves are considered. The excitable element can exhibit multiple periodicity in certain range of coupling strengths. Histograms of the inter spike intervals are measured to quantify the weights of different multiple periods and the associated system memory.
Second, oscillatory or excitable phase element driven by an external uniform rotator is investigated as a function of the coupling strength g. The excitable or oscillator phase element can exhibit frequency locked states in certain range of g. The frequency of the driven element shows a maximum as g increases. Remarkably, the driven element can exhibit a maximal locked frequency several times that of its intrinsic frequency or the driving frequency. Simple model can produce large frequency enhancement, with well-defined integer multiple frequency locked states, the frequency locked at m∙Ω state corresponds to period-m motion.

中文摘要 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
英文摘要 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
目錄 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
圖目錄 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
一、 介紹 . . . . . . . . . . . . . . . . . . . . . . . . 1
1-1 研究動機 . . . . . . . . . . . . . . . . . . . . . . 1
1-2 真實系統 . . . . . . . . . . . . . . . . . . . . . . 2
1-3 同步 (Synchronization) . . . . . . . . . . . . . . 3
1-4 理論背景 : 動力學系統 . . . . . . . . . . . . . . 4
1-4-1 FitzHugh-Nagumo model . . . . . . . . . . . . . 4
1-4-2 相干共振 (Coherence Resonance) . . . . . . . . 6
1-4-3 Phase model . . . . . . . . . . . . . . . . . . . . 7
二、 週期性驅動力對 FitzHugh-Nagumo model 影響
之探討 . . . . . . . . . . . . . . . . . . . . . . . 13
2-1 數值分析方法 . . . . . . . . . . . . . . . . . . . 13
2-1-1 模型 . . . . . . . . . . . . . . . . . . . . . . . . 13
2-1-2 模擬步驟 . . . . . . . . . . . . . . . . . . . . . . 13
2-2 數值分析結果 . . . . . . . . . . . . . . . . . . . 13
2-2-1 方波驅動 FHN model . . . . . . . . . . . . . . . 14
2-2-2 餘弦波驅動 FHN model . . . . . . . . . . . . . 21
2-2-3 三角波驅動 FHN model . . . . . . . . . . . . . 31
三、 週期性驅動力對相模型影響之探討 . . . . . . . . 39
3-1 數值分析方法 . . . . . . . . . . . . . . . . . . . 39
3-1-1 模型 . . . . . . . . . . . . . . . . . . . . . . . . 39
3-1-2 模擬步驟 . . . . . . . . . . . . . . . . . . . . . . 40
3-2 數值分析結果 . . . . . . . . . . . . . . . . . . . 40
v3-2-1 週期性驅動力對相振子的影響 . . . . . . . . . . 40
3-2-2 週期性驅動力對可激發相單元的影響 . . . . . . 42
3-2-3 拓展耦合項，週期性驅動力對相模型之探討 . . 43
四、 討論 . . . . . . . . . . . . . . . . . . . . . . . . 55
4-1 FHN 模型週期比例關係之探討 . . . . . . . . . . 55
4-2 phase model 中鎖頻比值之探討 . . . . . . . . . 57
4-3 circle map 與 phase model 之比較 . . . . . . . . 59
五、 結論與未來展望 . . . . . . . . . . . . . . . . . . 63
5-1 結論 . . . . . . . . . . . . . . . . . . . . . . . . 63
5-2 未來展望 . . . . . . . . . . . . . . . . . . . . . . 64
參考文獻 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

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