# From Individual to Collective Behaviour in Large-Scale, Complex Systems

Lead Research Organisation: University of Manchester
Department Name: Computer Science

### Abstract

When subjects like physics or chemistry are taught in schools, mathsis used to explain the theory behind different effects, so that theseeffects can be summarised neatly in terms of equations. This is notthe way that biology or all kinds of other subjects aretaught. Although many people think of physics and chemistry as hard,in fact the things they describe are in many ways simpler than saybiology or the study of how humans behave. For example, when a ball isthrown into the air it follows a curve, and if we can predict whatthat curve is, that usually tells us what we want to know about howthe ball moves. But suppose that we want to calculate how bees movetogether in a swarm of bees, or make up a chart of what-eats-what in alake. It's difficult to see how we could write down maths for this,because there are so many different things to describe, and each oneis affecting others, so the equations would become enormous. Systemssuch as these are called complex systems.The swarm of bees is a good example of how hard this can be. If youlook closely at the swarm on the tree trunk, all you will see is aseething mass of bees pushing and shoving each other. Occasionally,bees will leave the swarm and fly off, or others may arrive back atthe swarm having been on a journey somewhere. After a time (usually acouple of hours) all the bees will leave the tree trunk and fly offtogether to a place (a hollow tree, for example) where they will setup their new home. So, despite the fact it is made up of tens ofthousands of individual bees - each of which in more usualcircumstances behaves as if it has a mind of its own - somehow, theswarm as a whole finds out about good nest sites in the area and thendecides on the best one. How does all this pushing and shoving by the25,000 bees in a swarm result in such organised behaviour? Actually,this is kind of effect - where lots of things behave as if they werepart of some big whole - is a quite common. The flow of people goingto a football match and schools of fish swimming in the sea arefamiliar examples. This kind of behaviour has been called emergentbehaviour because it seems to emerge when lots of individuals are ableto interact with each other in particular ways. In the case of thebees what is happening is that the queen bee produces a perfume whichattracts the other bees to her; the bees cluster together because eachindividual tries to ensure that she can smell the perfume of the queenbee strongly. In the case of schooling fish, each fish can see itsfriends nearby and tries to swim in such a way that it keeps them inview.Many people believe that there are simple rules which are at the heartof these systems, and it just the fact that many things areinteracting together that gives rise to the complex behaviour we seein the real world. Although the maths we learn at school can't reallybe applied to these systems, a combination of the use of computers andmore advanced mathematical ideas can. Computers have become sopowerful recently, that we can use them to see if many thingsinteracting together in a simple way can really give rise to complexsystems that we see in the world around us. This is such a new idea,and involves things which are so different to what is taught inschools and universities that we think that it's a good idea to run asummer school where experts who work in this area can pass on theirunderstanding of complex systems to those who want to learn about thisnew area. Our plan is not only to have lectures, but to run projectswhere students at the school can learn by trying out ideas forthemselves.

### Publications

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Schläpfer M (2009) Complex Sciences

Boland RP (2009) Limit cycles, complex Floquet multipliers, and intrinsic noise. in Physical review. E, Statistical, nonlinear, and soft matter physics