Complex SystemsComplex Networks

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Complex Systems

What is the definition of complex systems?

Is there any difference between the complex systems and complicated systems?

Ants

forager

Nest maintenance worker patroller

Ants

Task allocation a process of continual adjustmentThe number of workers engaged in a specific task appropriate to the current conditionThe queen does not decide which worker does what! Small piles of the mixed seed are placed outside the nest

mound Away from the foraging trails In front of scouting patrollers active recruitment of foragers takes place

Toothpicks are placed near the nest entrance the number of nest maintenance workers increases

The task allocation achieved without any central control. The individual ant only perceives local information from the

ants nearby through chemical and tactile communication.This cooperative behavior of an ant colony results from local interaction between its members not from central controller emergent behavior

Emergent behavior

Defined as a large scale effects of locally interacting agents that are often surprising and hard to predict even in the case of simple interactions. Cannot predict the emergent behavior just by

analyzing the interaction between each element.

A system such as an ant colony, which consists of large populations of connected agent (that is, collections of interacting elements), is said to be complex if there exists an emergent global dynamics resulting from the actions of its parts rather than being imposing a central controller.

Complex Systems

From Sync by Steven Strogatz: "Every decade or so, a grandiose theory comes along, bearing similar aspirations and often brandishing an ominous-sounding C-name. In the 1960 it was cybernetics. In the '70s it was catastrophe theory. Then came chaos theory in the '80s and complexity theory in the '90s." Various informal descriptions of complex systems have been put forward, and these may give some insight into their properties. A special edition of Science about complex systems Science Vol. 284. No. 5411 (1999). highlighted several of these:A complex system is a highly structured system, which shows structure with variations (Goldenfeld and Kadanoff) A complex system is one whose evolution is very sensitive to initial conditions or to small perturbations, one in which the number of independent interacting components is large, or one in which there are multiple pathways by which the system can evolve (Whitesides and Ismagilov) A complex system is one that by design or function or both is difficult to understand and verify (Weng, Bhalla and Iyengar) A complex system is one in which there are multiple interactions between many different components (D. Rind) Complex systems are systems in process that constantly evolve and unfold over time (W. Brian Arthur).

SummaryProperties of Complex Systemslarge number of elements in the systemNonlinear interaction between each elementEmergent behavior– Universal behavior or order Collective behavior The behavior which cannot be predicted from

the interaction between each elementFeedback interactionAdaptationOpen SystemEdge of Chaos : Self-Organizing systemMore is Different.

Related Topics

Complex systems

chaos

Non-lineardynamics

Social Systems

StatisticalMechanics

Fractal ComputerScience

Networks

Bio-systems

ExamplesFractals in NatureFractals in Nature

Examples

Nonlinear SystemsNonlinear Systems Strange attractorsStrange attractors

A Few Good Man

Robert Wagner

Austin Powers: The spy who shagged me

Wild Things

Let’s make it legal

Barry Norton

What Price Glory

Monsieur Verdoux

Examples생물계생물계

Example경제계경제계

Examples

Synchronization of average velocities in neighboring lanes in congested trafficOn a crowded sidewalk, pedestrians walking in opposite directions tends to form lanes along which walkers move in the same directionSocial networks: citation networks, WWWStock market

How to study the complex systems

Assume a simplified system Identical elements

Representative agent model in microeconomics Each agent has the same properties to maximize its

efficiency

Probabilistic interactions or movements Brownian motion by random walk

Complexity

Complexity—the amount of information to characterize a systemComplexity measure A measure to quantify the complexity

Ex. Computational complexity, information complexity Kolmogorov measure—complexity measure of a strin

g : Ziv-Lepel algorithm The length of the program to generate the string

Grassberger measure: forecast complexity Excess entropy

Complexity

The complelxity can be changed by scale.Small scale increase the complexity

Emergent: Macroscopic order from Complex Dynamics

Power Law – Scale invariant universality Earthquake: Gutenberg-Richter’s law

Energy of the earthquake~1/frequency

The power-law implies that there is some universal law which governs the earthquake, regardless of the energy scale.

Pareto’s Principle

The universal law in social and economic system.80-20 rule 80% of income in Italy is received by 20%

of Italian population. 80% of consequences stem from 20% of

the causes. The same rule has been observed over

many different countries which have different histories and social environments.

Economics

Mandelbrot Study the price changes of cotton Power-law The price change cannot be described by random walk or

normal distribution The similar behavior is found in many stock exchanges, foreign

exchanges and on-line markets

Zipf’s LawOriginated from Linguistics The frequency of any word is inversely proportional to its ranks in the

frequency table.The same law can be found in the residence distribution of the democratic countries. (Not in the socialist states)This demonstrate that the free movement can create some universal law

Other Examples

And others

Distribution of the file size transmitted through the InternetSize of the instructions in computerSize of the sand on the beachNumber of species in each genusDegree distribution of the Internet, www, etc.