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.