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## Complex System Science

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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

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

Emergence or Self-Organisation

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

~ 100 km

~ 10 cm

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

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 F&M reporting rules may have delayed the isolation of infectious animals.

The relationship between these actions and the epidemiology of F&M was not appreciated in advance (at least where it mattered) because the livestock industry was not viewed as an integrated system.

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

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

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

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)

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)

What do we mean by stable states?

Linear dynamics Non-linear dynamics Boundaries of Strange

Periodic attractor Strange Attractor Attractors are Fractal

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

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 T+1 is determined by its own state and that of its two neighbours at time T

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

T=0

T=1

T=2

Or by changes in the ‘wiring’ of the network

The Cellular Automaton as a computer:Evolving the local rules that will perform a computational task by applying a global selection pressure

T=0

T=1

T=2

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

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

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.

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.

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)

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)

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.

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