Systems Theory Tiago Garcia de Senna Carneiro Pedro Ribeiro de Andrade Gilberto Câmara Münster, 2014

General Systems Theory  Provides a unified classification for scientific knowledge.  Enunciated by biologist Ludwig Von Bertalanffy :  1920s: earliest developments  1937: Charles Morris Philosophy Seminar, University of Chicago  1950: “An Outline of General Systems Theory”, Journal for the Philosophy of Science  Scientists that introduced Systems Theory in their fields:  Parsons, sociologist (1951)  J.G Miller, psychiatrist & psychologist (1955)  Boulding, economist (1956)  Rapoport, mathematician (1956)  Ashby, bacteriologist (1958) Karl Ludwig von Bertalanffy (September 19, 1901, Atzgersdorf near Vienna – June 12, 1972, Buffalo, New York) was an Austrian-born biologist known as one of the founders of General Systems Theory.

The Ratio Club

 A small informal dining club of young psychologists, physiologists, mathematicians and engineers who met to discuss issues in cybernetics (No professors, just amateurs.)  The idea of the club arose from a symposium on animal behaviour held by the Society of Experimental Biology in Cambridge, July  Ration in Latin is "computation or the faculty of mind which calculates, plans and reasons".  Started after the publications:  Norbert, Wiener - Cybernetics: Or Control and Communication in the Animal and the Machine.  Claude E. Shannon - A Mathematical Theory of Communication. (using tools in probability theory developed by Norbert Wiener).  W. Ross Ashby (London, 6 September 1903 – 15 November 1972) was an English psychiatrist and a most influential reseacher in cybernetics. His book named Introduction to Cybernetics (1958) dealt primarily with homeostatic processes within living organisms.  Alan Turing FRS ( ) is universally regarded as one of the fathers of both computer science and artificial intelligence..

How reality is conceived  Any measurable part of reality can be modelled as a system  Systems are represented as stocks and flows  Stocks represent storages of energy, matter, or information  Flows connect and transport stocks  Every system has a goal (survive).  Real systems are opened only theoretical ones are closed Environment System 2 System 3 System 1 System 4

How do we study systems? Identify the components Determine the nature of the interactions between components

What is a System?  Definition : A system is a group of components with different functions, which interact with each other  Example: The climate system includes the atmosphere, oceans, polar caps, clouds, vegetation…and lots of other things

Earth as a system

A system  Can you identify parts? and  Do the parts affect each other? and  Do the parts together produce an effect that is different from the effect of each part on its own? and perhaps  Does the effect, the behavior over time, persist in a variety of circumstances? Source: (Meadows, 2008)

Systems can grow in different ways... forever... explode... stabilize...

Run code #1 – Linear Growth

Feedbacks  Feedback is a flow of information that allows a system affect itself  Essential to systems be able to reach their goal Inflow Outflow System Feedback Formalized by Norbert Wiener (November 26, 1894 – March 18, 1964), an American mathematician and philosopher. He was Professor of Mathematics at MIT. Cybernetics is a transdisciplinary[1] approach for exploring regulatory systems, their structures, constraints, and possibilities. 1948, Cybernetics: Or Control and Communication in the Animal and the Machine. Paris, (Hermann & Cie) & Camb. Mass. (MIT Press) ISBN ; 2nd revised ed

Population growth Births Deaths Fertility Mortality Population

Reinforcing feedbacks  Also named: positive, self-reinforcing, discrepancy- enhancing, degenerative  Self-enhancing behavior that leads to growth or even collapses

Run code #2 – Exponential Growth

Balancing feedback  Also named: negative, self-correcting, discrepancy- reducing, regenerative  Equilibrating or goal-seeking structures

Homeostasis  It is a tendency that all systems have to maintain their equilibrium state through negative feedbacks Initial condition = 3.2 Initial condition = 8

Run code #3 – Homeostasis

Equilibrium state (some times steady-state)  Equilibrium means a state of balance.  There are no net flows of matter or of energy  Input flow == Output flow Inflow Outflow System

An Unstable Equilibrium State low resilience

An Unstable Equilibrium State Perturbation

When pushed by a perturbation, an unstable equilibrium state shifts to a new, stable state.

A Stable Equilibrium State higher resilience

A Stable Equilibrium State Perturbation

When pushed by a perturbation, a stable equilibrium state, returns to (or near) the original state.

Run code #4 – Logistic Growth

Verify and analyse models with visualizations  TerraME provides you different types of Observers  However, it can only observes TerraME types: Cell, Agent, CellularSpace, Timer, Environment, etc.

Ant agents eat sugar on a cellular space

Observers for massive visualizations Dedicated high-performance hardware and remote graphical workstations Rodrigues, A. J. C., Carneiro, T. G. S., and Andrade, P. R. An Extensible Real-time Visualization Pipeline for Dynamic Spatial Modeling. Journal of Information and Data Management. 4(2), p , 2013.

Run codes #5, #6 – Logistic Growth

Discrete & Continuous Systems  Discrete systems jump from one state to other without intermadiate valuas, like the traffic light.  Continuous system change from a state to other going through all intermadiate states, like the speed of a car.  Depending on your point of view you can model a system as discrete or continuos, like a lift. h t+1 =h t ± 1 = ± 0.1 h

There are different types of equlibrium  Discrete systems:  Fixed point - System converges to a one-dimension fixed value.  N-dimensional attractors – System converges to attractors composed by several N fixed points  Deterministic CAOS – System is locked in a high dimensional attractor composed theorically by a infinite number of fixed points and will never repeat itself (this is the caos).

Run codes #7 – Discrete Logistic Growth  As the system is discrete we should use a difference equation istead of a differential equation:

Logistic Map  From smooth behavior to deterministic caos through duplication of periods.  Feigenbaum, M. (1983) – in Physics.  May, R. (1976) – in Ecology.

Discrete Growth – It is no error propagation! (a) r = 1,2, (b) r = 3,0, (c) r = 3,5 e (d) r = 4,0.

There are different types of equlibrium  Cotinuous systems:  One single system  Static equilibrium - System converges to a one-dimension fixed value.  Coupled sytems (like prey-predator)  Static equilibrium - System converges to a one-dimension fixed value.  Dynamic equilibrium – System converges to cyclical behavior and keep repeating itself  Erratic outcomes of deterministics rules should be treated as error propagation in the integration method

Run code #8 – Contiuous System

How CONTINUOUS systems grow?  Linear growth  Exponential growth  Logistic growth N r k

How to implement stochastic models?  Create a random object that is able to generate numbers in a uniform distribution random = Random() probability density function  Call function number(a, b) to generate real numbers within the interval [a, b]: n = random:number(0,1)  Call function integer(a,b) to generate integers within the interval [a,b]: n = random:integer(10,20)

How to implement stochastic models? random = Random() counter = 0 for t = 1, 1000 do local n = random:number(0, 1) if ( n <= 0.3) then -- try counter = counter + 1 end print( (counter/1000) * 100 ) -- 30%

Run codes #9 and #10 – Stochastic process

Coupled systems – Dynamic Equilibrium

Run code #11 – Prey-predator model

System Dynamics & Dynamo Language Jay W. Forrester (Nebraska, 1918… ) is know as the founder of System Dynamics, which deals with the simulation of interactions between components in dynamic systems The language Dynamo was developed under direction of Jay Wright Forrester in the late 1950s at M.I.T.. A system in Modelica

Dynamo Building Blocks  Stocks  Flows  Information Links  Decision Points  Converters  Auxiliary Variables

Stocks  “ Things ” that accumulate in a system  Physical or non-physical things  Value is a quantity or level  Persistent (remain even if all flows stop)  Conservation (stock units enter from environment and return to environment)

Flows  Movement of “ things ” in and out of stocks  Not persistent (can be stopped and started)  Value is a rate of change (will always have a time dimension)  Flow unit = stock unit / time  The unit of measurement for a flow will always be the unit of measurement of a stock divided by an element of time

Stock and Flow Diagram  Stocks in boxes  Flows as straight double arrows  Information Links as thin curved arrows  Decision Points as closed in X

Control Material Flaw to Stock Add New information Send information from the Stock Control Material Flaw from Stock Stock System Dynamics Modelling

Tools for system dynamics  Dinamo  Vensim  Simile  STELLA