指南針和牛蛙心臓混沌動力學控制之研究｜國立中央大學博碩士論文系統

簡易檢索 / 詳目顯示

回結果列表

研究生：	柯佩蓮 Nurra Keprin
論文名稱：	指南針和牛蛙心臓混沌動力學控制之研究 Controlling Chaotic Dynamics in a Compass and Cardiac Tissues of a Frog
指導教授：	陳志強黎璧賢
口試委員:
學位類別：	碩士 Master
系所名稱：	理學院 - 生物物理研究所 Graduate Institute of Biophysics
論文出版年：	2017
畢業學年度：	105
語文別：	英文
論文頁數：	76
中文關鍵詞：	牛蛙心臟、混沌指南針、心跳強弱交替、回饋控制
外文關鍵詞：	Frog's heart, Chaotic Compass, Alternans, Feedback control
相關次數：	點閱：11 下載：0
分享至:	分享至facebook 分享至twitter

查詢本校圖書館目錄查詢臺灣博碩士論文知識加值系統勘誤回報

物理及生物的非線性系統在週期性刺激下，會產生混沌行為，此混沌行為可透過外界控制以避免系統產生不規則行為。在這篇論文當中，我們運用最近提出的回饋控制方法¬—T±ε(先前用來降低大鼠心跳強弱交替的現象[24])，來控制生物與物理系統，分別為控制牛蛙心臟組織的跳動，與指南針的轉動。在兩個系統中，我們皆成功的抑制系統倍週期現象。對於心臟組織，控制方法為T±ε，也就是刺激周期為一固定常數Ｔ外加微小回饋擾動±ε；而對於指南針，回饋系統為電壓，稱為Ａ±ε，也就是刺激為一固定電壓A外加微小回饋擾動±ε。在指南針系統，ε值必須大於一臨界值才能有效的控制倍週期現象。更進一步，利用Ａ±ε 的控制方法，我們發現高週期的狀態可被控制到低週期或是混沌狀態，又或是非週期狀態可被控制成週期狀態。最後，我們利用數值遞迴映射(單峰映射與心臟復位映射)驗證這些結果，並以微分方程描述此非線性系統。

Chaotic behaviors exist naturally in both physical and biological nonlinear systems
when they are driven periodically. These chaotic behaviors can be undesirable and control
is needed for the external drive to avoid irregular behaviors in these systems. We apply a
recently proposed feedback control method, known as T ± ε (developed for the suppression
of alternans in the hearts of rats [24]), to control the beating of the cardiac tissues of a bull
frog’s heart and the motion of a compass when they are driven externally by a periodic
signal with period T. In both cases, we suppress successfully the period doubling dynamics
of both systems. For the cardiac tissues, the control is the same as the T ± ε with the small
feedback perturbations on the driving period. However, for the compass, small feedback
perturbations are applied to the driving voltage A2 and we call this A ± ε method. In
this later case, there seem to be a critical epsilon such that suppression of period doubling
can be effective only when epsilon is larger than a critical value. Furthermore, by using
this A ± ε control method for the periodically driven compass, we find that high periods
states can be controlled to low periods states and even chaotic or non-periodic states can
be tamed to periodic states. These results are also verified numerically by using iterated
maps (Logistic Map and Cardiac Restitution Map) and a system differential equation to
describe these nonlinear systems.

page
摘要 iii
Abstract v
Acknowledgement vii
Contents ix
Introduction 1
1 Background. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 Nonlinearity and Chaos : Stability Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2.1 Bifurcation Diagram and Poincare Map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
3 Controlling Chaos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.1 OGY Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.2 Pyragas Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.3 Feedback Control T ± ε and A ± ε . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
4 Differential Equation Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
5 Logistic Map and Cardiac Restitution Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Method 17
1 Frog Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.1 Set-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.2 Measurement and Pulse Generator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.3 Experimental Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2 Compass Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.1 Set-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.2 Calibration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.3 Error Estimate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
Result 31
1 Reproducing Published Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
1.1 Frog Experiment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
1.2 Compass Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2 Period-doubling Suppression Experiments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.1 Frog Experiment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.2 Compass Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
Conclusion 47
A Code 55
A.1 IDL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
                                

[1] Edward Ott, Celso Grebogi, and James A Yorke. Controlling chaos. Physical review
letters, 64(11):1196, 1990.
[2] Steven H Strogatz. Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering. Westview press, 2014.
[3] Ying-Cheng Lai. Controlling complex, non-linear dynamical networks. National Science Review, 1(3):339– 341, 2014.
[4] Schaffer, W.M. and Kot, M., 1985. Do strange attractors govern ecological systems?.
BioScience, 35(6), pp.342-350.
[5] McMillan, D.G., 2003. Non‐linear Predictability of UK Stock Market Returns. Oxford
Bulletin of Economics and Statistics, 65(5), pp.557-573.
[6] Easterling, D.R. and Wehner, M.F., 2009. Is the climate warming or cooling?. Geophysical Research Letters, 36(8).
[7] Easterling, D.R., Meehl, G.A., Parmesan, C., Changnon, S.A., Karl, T.R. and
Mearns, L.O., 2000. Climate extremes: observations, modeling, and impacts. science,
289(5487), pp.2068-2074.
[8] Rohr, J.R. and Raffel, T.R., 2010. Linking global climate and temperature variability
to widespread amphibian declines putatively caused by disease. Proceedings of the
National Academy of Sciences, 107(18), pp.8269-8274.
[9] Xia, H., Zhao, X., Bains, J. and Wortham, D.C., 2009, September. Influence of channel
blockers on cardiac alternans. In Engineering in Medicine and Biology Society, 2009.
EMBC 2009. Annual International Conference of the IEEE (pp. 2823-2826). IEEE.
[10] Marc R. Roussel. Maps: Stability and bifurcation analysis. 2005.
[11] May, R.M., 1976. Simple mathematical models with very complicated dynamics.
Nature, 261(5560), pp.459-467.
[12] Mark J Ballico, Mark L Sawley, and Frederic Skiff. The bipolar motor: A simple
demonstration of deterministic chaos. American Journal of Physics, 58(1):58– 61,
1990.
[13] M Guevara, Leon Glass, and Alvin Shrier. Phase locking, period-doubling bifurcations, and irregular dynamics in periodically stimulated cardiac cells. Oecologia
(Berlin), 19:75, 1975.
[14] Guillermo V Savino, Lilia Romanelli, Diego L Gonzalez, Oreste Piro, and Max E
Valentinuzzi. Evidence for chaotic behavior in driven ventricles. Biophysical journal,
56(2):273– 280, 1989.
[15] Alan Garfinkel. Controlling cardiac chaos. Science, 1992.
[16] Berger, C.M., Zhao, X., Schaeffer, D.G., Dobrovolny, H.M., Krassowska, W. and
Gauthier, D.J., 2007. Period-doubling bifurcation to alternans in paced cardiac tissue: crossover from smooth to border-collision characteristics. Physical review letters,
99(5), p.058101.
[17] Sandra RFSM Gois and Marcelo A Savi. An analysis of heart rhythm dynamics using
a three-coupled oscillator model. Chaos, Solitons, Fractals, 41(5):2553– 2565, 2009.
[18] V Croquette and C Poitou. Cascade of period doubling bifurcations and large stochasticity in the motions of a compass. Journal de Physique Lettres, 42(24):537– 539, 1981.
[19] William L Ditto, Steven N Rauseo, and Mark L Spano. Experimental control of
chaos. Physical Review Letters, 65(26):3211, 1990.
[20] E R Hunt. Stabilizing high-period orbits in a chaotic system: The diode resonator.
Physical Review Letters, 67(15):1953, 1991.
[21] Roberta Hansen and Graciela Adriana González. Controlling chaotic maps by feedback control modulation. arXiv preprint arXiv:1605.06860, 2016.
[22] Kestutis Pyragas. Continuous control of chaos by self-controlling feedback. Physics
letters A, 170(6):421– 428, 1992.
[23] B.C. Kuo, Sistemas de Control Autom´atico, Prentice Hall, 1995
[24] Duy-Manh Le, YT Lin, YH Yang, Pik-Yin Lai, and CK Chan. Cardiac alternans
reduction by chaotic attractors in T ± ε feedback control. EPL (Europhysics Letters),
117(5):50001, 2017.
[25] Ashikaga, H., Aguilar-Rodríguez, J., Gorsky, S., Lusczek, E., Marquitti, F.M.D.,
Thompson, B., Wu, D. and Garland, J., 2015. Modelling the heart as a communication
system. Journal of The Royal Society Interface, 12(105), p.20141201.
[26] Rafael Gonzalez, C. and Woods, R., 2002. Digital image processing. Pearson Education.
[27] Schanne, O.F., Ruiz, P. and Ceretti, E., 1977. Impedance measurements in biological
cells. Wiley.
[28] Kalb, S.S., Dobrovolny, H.M., Tolkacheva, E.G., Idriss, S.F., Krassowska, W. and
Gauthier, D.J., 2004. The restitution portrait. Journal of cardiovascular electrophysiology, 15(6), pp.698-709.
[29] Sardanyés, Josep, and Ricard V. Solé. ”Ghosts in the origins of life?.” International
Journal of Bifurcation and Chaos 16.09 (2006): 2761-2765.

簡易檢索 / 詳目顯示

相關論文