Complex System Science. John Finnigan CSIRO Atmospheric Research. Contents. Complex systems Science Systems Complexity-the idea of emergent structure Farming systems as â€˜Complex Adaptive Systemsâ€™ Three Approaches to Understanding Network Theory Cellular Automata Agent Based Models
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CSIRO Atmospheric Research
Has two elements:
~ 100 km
~ 10 cm
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.
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
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:
(Figs from Scheffer et al, 2001, Nature)
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)
Linear dynamics Non-linear dynamics Boundaries of Strange
Periodic attractor Strange Attractor Attractors are Fractal
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
Dynamics on networks can evolve either by changes in the interaction rules
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
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
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