Complex System Science

1
Complex System Science

• John Finnigan
• CSIRO Atmospheric Research

2
Contents

• Complex systems Science
• Systems
• Complexity-the idea of emergent structure
• Farming systems as Complex Adaptive Systems
• Three Approaches to Understanding
• Network Theory
• Cellular Automata
• Agent Based Models
• Summary
• The CSIRO Centre for Complex Systems Science

3
Complex System Science

• Has two elements
• Systems-collections of interacting things
• Complexity-the essence of which is the property
  of self-organisation or emergence of structure
  from the interaction between the constituent
  parts of the system

4
Emergence or Self-Organisation

• We recognise this phenomenon over a vast range of
  physical scales and degrees of complexity
• From Galaxies 106 Light Years

5
(No Transcript)
6
To cyclones 100 km
7
And Chemical reactions 10 cm
8
(No Transcript)
9
(No Transcript)
10
(No Transcript)
11
(No Transcript)
12
(No Transcript)
13
To Gene expression and cell interaction
Amoeba
Ribosome
Root Tip
E Coli
14
The processing of information by the brain
15
To animal societies and the emergence of culture
16
And the social artefacts of human society such as
economies
17
The Concept of Self-Organisation has consequences
at several levels

• At the whole system level (in the present case,
  farming systems) it means that no one is in
  charge and optimal or command and control
  solutions to system problems usually fail (sooner
  or later)
• At the level of analysis, self organising
  processes provide us with powerful tools

18
Foot and Mouth Disease in the UK An example of
failure caused by focussing on one part of the
system and ignoring the links between biophysics
and economics
Economic rationalization of abattoirs and bizarre
EU subsidies increased the connections between
herds to a critical point. Changes to FM
reporting rules may have delayed the isolation of
infectious animals. The relationship between
these actions and the epidemiology of FM was not
appreciated in advance (at least where it
mattered) because the livestock industry was not
viewed as an integrated system.
19
Farming Systems at the gross level involve
Economics, People, their Social Networks as well
as Biophysics such as hydrology, soil science,
Agronomy and Biology.

• We can attempt to understand and model the whole
  system or parts of it
• To model the whole system we need first a mental
  map and then some techniques to capture the parts
  and interactions of the mental map

20
A regional scale social-ecological system
including farming, as a complex adaptive system
In a CAS, there is no Fat Controller. The system
behaviour is an emergent property
Climate
The Market
21
(No Transcript)
22
(No Transcript)
23
We can build models of Complex adaptive Systems
using techniques like Agent based Modelling but
to understand and predict their behaviour, we
need a science of systems

• The understanding we need is coming from a
  evolving blend of at least three different
  approaches
• Dynamical Systems Theory
• Network Theory
• Evolutionary or adaptive computing

24
1 Studying Ecosystems as dynamical systems

• A minimal model of an ecosystem describes the
  change over time of ecosystem state.
• The trajectories indicate stable states of the
  ecosystem as external conditions change
• Ecosystems that display two (or more) alternative
  stable states include
• lakes(oligotrophic/eutrophic),
• grasslands/woodlands,
• coral reefs (pristine/algal covered),
• marine ecosystems as measured in fish catch.

(Figs from Scheffer et al, 2001, Nature)
25
Basins of attraction and Ecosystem Resilience
A minimal model of an ecosystem describes the
change over time of an unwanted ecosystem
property, x such as lake turbidity a
represents an environmental factor that promotes
x, b represents the rate at which x decays in
the system, r is the rate at which x recovers
again as a function f of x The form of f(x)
determines whether multiple stable states or
attractors will exist
(Figs from Scheffer et al, 2001, Nature)
26
What do we mean by stable states?
Linear dynamics Non-linear dynamics
Boundaries of Strange Periodic attractor
Strange Attractor Attractors are Fractal
27
We can represent most systems as networks with
interactions across the links-Network Topologies
control System behaviour
Regular Network each node has the same number of
connections
Homogeneous network Number of connections per
node varies but there is a clear average value.
Networks like this can result from randomly
connecting nodes. Near the phase transition they
are vulnerable to random removal of links
Heterogeneous or scale free network There is
no average number of connections per node
Living networks that grow by accretion often have
this dendritic form. They are resilient to
random removal of links but vulnerable to a
targeted attack that removes a key node
28
3 Adaptive Systems can be illustrated simply
using Cellular Automata. CAs are Systems that
evolve on lattices according to local interaction
rules
The simplest rules the state of a cell at time
T1 is determined by its own state and that of
its two neighbours at time T
29
Discretization of PDEs yields Cellular Automata
Advection-diffusion equation
tn tn1
30
We can form new types of Cellular Automata by
changing the interaction rules or the wiring or
both
Dynamics on networks can evolve either by changes
in the interaction rules
T0 T1 T2
Or by changes in the wiring of the network
31
The Cellular Automaton as a computerEvolving
the local rules that will perform a computational
task by applying a global selection pressure
T0 T1 T2
The colour that a cell adopts at the next
timestep depends only on the colours of itself
and its neighbours at the present time step
Rules are recombined (bred) and selected
according to Darwinian principles to find the set
of local rules that will solve the density problem
32
Moving Away from Classical Mathematics

• With complete freedom to stipulate rules and
  wiring between elements of our CAs in the virtual
  world of the computer and then to let them evolve
  as part of the computation, we can form
  mathematical objects that are very difficult to
  capture using the approaches of conventional
  mathematics but which match very well what we
  observe in living systems.
• Agent Based Models exploit this freedom
• Analysis using network theory and similar
  techniques is leading to increasing understanding
  of these systems-but so far we have few general
  principles

33
Summary

• Complex Systems Science brings together systems
  approaches and a rapidly developing science of
  systems
• Rather than being any particular set of
  techniques it is primarily the adoption of a
  different point of view
• That is, to admit the prevalence of self-
  organisation in complex systems together with the
  behaviours that flow from that and the techniques
  necessary to study it.

34
The CSIRO Centre for Complex Systems Science-A
Virtual Centre
The Core Group comprises a permanent Science
Director, a Communication and Training Manager,
Post Docs, PhDs and visitors. It interacts with
Division based projects to do basic research in
CSS. Projects are located within CSIRO Divisions
(and partner Institutions). A key function of
the Core group is to manage interaction between
the projects. The Core and the Division-based
Projects are closely networked.
35
The Compass of Complex System Science Projects
in the CSIRO Centre for CSS-1

• Inference of complex systems properties from
  fragmentary information (Mantle dynamics and
  mineralization State Space reconstruction)
• Ensemble Prediction of Atmospheric and
  Ocean-Atmosphere Regime Transitions (Dynamical
  Systems theory)
• The stability of the Southern Ocean overturning
  circulation (Dynamical Systems theory)
• Critical states in bushfires (Dynamical Systems
  theory, Agent Based Modelling)
• The effects of model structure and dimensionality
  on the emergent properties of ecosystem models
  (Estuarine systems Dynamical Systems theory,
  ABM)
• Rapid shifts in state and resilience in river
  systems (ABM)
• Targeting Drug-like properties in Chemical
  libraries (Genetic Algorithms, Evolutionary
  computing)

36
The Compass of Complex System Science Projects
in the CSIRO Centre for CSS-2

• Tracking Air Borne Chemical Signals (Fractal
  turbulence AI, ABM)
• Adaptation and resilience in regional
  socio-economic systems (Managed rangelands ABM)
• Multiscale modelling in Industrial and Natural
  systems (Lattice-Boltzmann methods, Non-Equil
  Thermodynamics)
• Interactions, information sharing and simulated
  reasoning of fishers in an agent-based, Bayesian
  network model of fishing behaviour (ABM)
• The Future of the Swan River Governance and
  Agent Based Modeling (ABM, Evolutionary game
  theory)
• Our National Electricity Market as a Complex
  Adaptive System (ABM)
• Links between resilience and information in
  complex adaptive systems (ABM, Evolutionary game
  theory)

37
The Purpose of This Workshop

• Is to bring together workers with awareness of
  the problems and workers with knowledge of CSS
  Techniques
• And to start a process of developing projects for
  future joint funding
• We plan a funding round built around the 2nd
  CSIRO CSS workshop in Sydney 27-29 August, 2003.