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复杂系统研究的科学基础. 自组织理论与动力学. 狄增如 北京师范大学管理学院系统科学系 北京师范大学复杂性研究中心 2010.7. I. Prigogine. H. Haken. 自组织理论. I. Progogine: Far-from-equilibrium studies led me to the conviction that irreversibility has a constructive role. It makes form. It

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复杂系统研究的科学基础

  • 自组织理论与动力学

狄增如

北京师范大学管理学院系统科学系

北京师范大学复杂性研究中心

2010.7


  • H. Haken


自组织理论

I. Progogine: Far-from-equilibrium studies

led me to the conviction that irreversibility

has a constructive role. It makes form. It

makes human beings.

自组织系统的主要特征:

1、开放系统,与环境有物质和能量交流;

2、组元众多,且存在非线性相互作用;

3、远离平衡态;

4、涨落是有序结构形成的触发器。


分支图

参数


生物进化树

生物、社会、经济等领域中的应用


系统演化的动力学描述

  • 关心系统演化的极限行为及其随环境条件的变化所导致的分支行为

  • 线性稳定性分析,分支理论,突变论


关于混沌 Chaos

古希腊与中国:混沌初开

20世纪80年代,混沌理论成为一个

新的、激动人心的科研领域

它将深刻地改变我们对自然及人类的认识



混沌的基本性质

对初值的敏感依赖性——蝴蝶效应

差之毫厘,失之千里

确定性系统中的随机行为

在不引入任何随机因素的情况下,一个

简单的系统可以产生非常不规则的行为

一种没有周期性的有序



分形结构 Fractal

分形:Logistic map, Lorenz attractor,

Mandelbrot set, Julia set


人体血管总体积<5%

肺的总面积>网球场

  • 股票分时走势图


为什么混沌如此引人注目?

 混沌揭示了简单性和复杂性、有序和无序

之间的精妙关联,从而沟通了科学与生活;

 一个遵循基本物理规律、确定论性的世界,

可以是无序的,具有复杂性和不可预测性;

 复杂现象的背后可能具有简单的规律;

 在任何层次上,我们对未来的理解和预测都是

有限的;

 混沌是非常漂亮的。


二十世纪物理学的重要进展

* 量子力学——微观世界

* 狭义与广义相对论——宏观世界

* 自组织与混沌——生命现象


The Cell Cycle

Nurse P. The incredible life and times of biological cells. Science 289:1711, 2000


Protein Micro-arrays

Detecting Protein Interaction/Biochemistry

Service RF. Protein arrays step out of the shadows. Science 289:1673, 2000




Stock Market: Levy分布——正态分布


Minority Game

Agent-based Computational Economics


案例研究:心脏中的动力学

UCLA Cardiology Division


CARDIAC FIBRILLATION

  • Ventricular fibrillation

    • 220,000 sudden deaths annually in U.S.

  • Atrial fibrillation

    • 6% of population over age 65

    • 1/3 of all strokes over age 65

    • doubled mortality rate


VT to VF

transition

VF

maintenance

VT

initiation

?

?

PVC Hypothesis

CAST

SWORD

SUDDEN CARDIAC DEATH




Ca2+

Na+

K+

-80 mV

T-tubules

T tubule

myofilaments


Ca2+ (10-20%)

Extracellular space

Ca channel

T-tubule membrane

Ca release channel

(Ryanodine receptor)

Ca2+

(80-90%)

SR Ca ATPase

Sarcoplasmic

reticulum

Ca2+


3D Confocal Image of T-tubule System

Courtesy of Joy Frank, PhD

& Alan Garfinkel, PhD

UClA Cardiovascular

Research Laboratory


Courtesy of Joy Frank, PhD

UCLA Cardiovascular

Research Laboratory


RyRs

DHPR

Ca

DHPRs

Ca

RyRs

Ca

SR Ca stores


Na+-Ca2+

Exchanger

SL Ca2+-

ATPase

Ca2+ (10-20%)

3Na+

Calsequestrin

Ca channel

T-tubular membrane

Ca release channel

(Ryanodine receptor)

Ca2+

Ca2+

(80-90%)

Sarcoplasmic

reticulum

SR Ca ATPase


Hodgkin AL, Huxley AF. A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. (Lond.) 1952;117:500-544.


mV membrane current and its application to conduction and excitation in nerve.

time(ms)


Cardiac Action Potential Model membrane current and its application to conduction and excitation in nerve.

dVm/dt = -S (Iionic + Iext)/ Cm

Zeng J, Laurita KR, Rosenbaum DS, Rudy Y. Circ. Res.77:140-152, (1995)


50000 membrane current and its application to conduction and excitation in nerve. steps in 4.43 seconds

20

0

-20

V (mV)

-40

-60

-80

-100

0

100

200

300

400

500

600

700

800

900

1000

TIME (msec)

2 ms

15 mA

=

Runge-Kutta 4th order, DT = .02 ms


FitzHugh-Nagumo membrane current and its application to conduction and excitation in nerve. Model:

Barkley Dynamics:

du/dt= f(u,v)=u(1-u)[u-(v+b)/a]/,

dv/dt=g(u,v)=u-v

u

1

g(u,v)=0

0.9

v

0.8

0.7

0.6

v= au-b

x, y

0.5

0.4

b

0.3

v

0.2

0.1

u

0

0

2

4

6

8

10

12

14

16

18

20

TIME


vanCapelle FJL, Durrer D. Computer simulation of arrhythmias in a network of coupled excitable elements. Circ. Res. 1980;47:454-466.


in a network of coupled excitable elements. Circ. Res. 1980;47:454-466.

V

=

-

+

I

/

C

D

V

Ñ

.

Ñ

ion

m

t

å

å

=

=

I

I

f

(

V

)

ion

k

k

Neumann

boundary

condition

:

r

.

=

n

V

0

Ñ


P in a network of coupled excitable elements. Circ. Res. 1980;47:454-466.

Plane Wave

S

Spiral Wave

SK

Spiral Wave Breakup


1 in a network of coupled excitable elements. Circ. Res. 1980;47:454-466.

2

What Causes The Waves To Break?

Traditional Answer: Pre-existing Tissue Heterogeneities

(anatomic or electrophysiological)

Slope < 1


APD in a network of coupled excitable elements. Circ. Res. 1980;47:454-466.

S2

S1

Diastolic Interval


Electrical Restitution (S1S2 Method) in a network of coupled excitable elements. Circ. Res. 1980;47:454-466.

APD Restitution CV Restitution

THE SLOPE!

>1 : + gain amplifier

<1 : - gain attentuator

Wavelength Is Also Controlled Dynamically by Electrical Restitution

(in the absence of pre-existing heterogeneities)


2 in a network of coupled excitable elements. Circ. Res. 1980;47:454-466.

1

3

Dynamic Wavebreak:

The Role of APD Restitution Steepness

Slope < 1

Slope > 1


in a network of coupled excitable elements. Circ. Res. 1980;47:454-466.X

Steep Slope

Shallow Slope

Y  X

Y

Y

Y < X

X


A in a network of coupled excitable elements. Circ. Res. 1980;47:454-466.

B

a

a

b

150

b

100

100

c

APD (ms)

APD (ms)

50

c

50

0

0

0

50

100

0

50

100

150

DI (ms)

DI (ms)

b

b

c

c

d

d

0

0

-40

-40

V (mV)

V (mV)

-80

-80

0

200

400

600

800

1000

1200

1400

0

200

400

600

800

1000

1200

1400

t (ms)

t (ms)


Reduction in a network of coupled excitable elements. Circ. Res. 1980;47:454-466.

Body EKG

Whole Heart

Myocyte

Channel

EKG

Current

Action potential

Electrical wave

Integration

Emergent parameters and properties:

APD restitution, CV restitution,

pre-existing heterogeneities,

spiral wave, spatiotemporal chaos

Research Approaches for VF


Methodology of 20 in a network of coupled excitable elements. Circ. Res. 1980;47:454-466.th Century Physics and Biology

Reductionism

Matter

Living Organisms

Macroeconomy

Transcription

Factors

Complexity

Self-organizing behavior

Pattern formation

What are theglobal parameters ?


Genomic Biology in the 21 in a network of coupled excitable elements. Circ. Res. 1980;47:454-466.st Century

Genome Letters: ‘abcdefghijklmnopqrstuvxyz’

Molecules (biophysics & Words: ‘cat’, ‘dog’, ‘mommy’, ‘daddy’

structural biology)

OrganellesSentences: ‘We, the people of the .…….the United States of America.’

Cells Paragraphs:‘It was the best of times, it was….. Thus did the year one ….’

OrgansChapters: Chapter 1. ‘Call me Ismael…’

Living organisms Books: War and Peaceby Leo Tolstoy


Biology or Physiology for the 21 in a network of coupled excitable elements. Circ. Res. 1980;47:454-466.st Century

Analogy with Physics of the 20th Century

20th Century Physics

Expt 1900 Theory Classical Physics

Expt 1905 Theory Special Relativity

Expt 1914 Theory General Relativity

Expt 1920’s Theory Quantum Mechanics

Expt 1930’s Theory Quantum Electrodynamics

Expt 1960’s Theory Quantum Chromodynamics

Expt 1980’s Theory String Theory

Expt 1990’s Theory M Theory

21st Century Physiology

Expt 2000 Theory The Genomes

Expt2100 TheorySecrets of Life


The four greatest questions pondered ever since the dawn of human civilization:

What’s for dinner?

Will she go out on a date with me?

What is nature?

20th Century Physics

M theory – the 11-dimensional universe that explains everything, but is beyond the scope of experimental verification (requires big bang conditions)

What is life?

21st Century Complexity

Answer as yet unknown, but approachable


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