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Significance Statement
‘Tipping points’ are the sudden and catastrophic changes in complex systems such as financial markets (market crashes), ecosystems (species extinctions), brain dynamics (epileptic seizures) and the climate (global climate change). There are two important questions we want to be able to answer about these changes: How close is the system to a tipping point? and can we navigate around a tipping point so that changes, if we cannot reverse them, at least occur more smoothly over a longer period of time? These are key questions because it is not always so important where we end up but it is sometimes the path we take to get there that matters. Take for example climate change, a sea level rise of 2 to 4 meters, shifting weather patterns reducing crop outputs or the loss of species diversity are more difficult issues to address if they happen too quickly for us to adapt. Taken over tens of thousands of years the geographical distribution of a culture can change as can the location of their resources, likewise over millions of years species die out while others can adapt and fill their vacated ecological niches. When these changes occur over mere decades or centuries though, the loss of biodiversity, the moving or restructuring of our cities, the changing of our crop locations and the infrastructure that supports them will cost us dearly in terms of our economies, our way of life and the lives of the people who will ultimately become climate refugees.
Two articles that have recently been published have attempted to answer some of these issues using simplified theoretical models in order to test wether or not such detection and navigation is possible in principle. The first article published in European Physical Journal B addresses the question of tipping point navigation: If we know a system is about to go through a tipping and it is not possible to directly reverse the process, what can we do to ‘nudge’ the system towards a safer path where changes happen more slowly?
The second article published in Physical Review Letters: http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.177203 addresses the question: What can we do to measure the current state of the system in order to discover how close we are to a tipping point such that we need to take action? Taken together these two articles begin to address the theoretical foundations on which to ask these questions in more practical situations with real data.
Journal Reference
Eur. Phys. J. B (2013) 86: 289.
Michael S. Harré, Simon R. Atkinson and Liaquat Hossain.
Complex Systems Group, Faculty of Engineering and Information Technology, The University of Sydney, NSW 2006 Sydney, Australia.
Abstract
Tipping points are a common occurrence in complex adaptive systems. In such systems feedback dynamics strongly influence equilibrium points and they are one of the principal concerns of research in this area. Tipping points occur as small changes in system parameters result in disproportionately large changes in the global properties of the system. In order to show how tipping points might be managed we use the Maximum Entropy (MaxEnt) method developed by Jaynes to find the fixed points of an economic system in two different ways. In the first, economic agents optimise their choices based solely on their personal benefits. In the second they optimise the total benefits of the system, taking into account the effects of all agent’s actions. The effect is to move the game from a recently introduced dual localised Lagrangian problem to that of a single global Lagrangian. This leads to two distinctly different but related solutions where localised optimisation provides more flexibility than global optimisation. This added flexibility allows an economic system to be managed by adjusting the relationship between macro parameters, in this sense such manipulations provide for the possibility of “steering” an economy around potential disasters.
