Boltzmann, Lotka and Volterra and spatial structural evolution: an integrated methodology for some dynamical systems

Wilson, Alan

doi:10.1098/rsif.2007.1288

Cited by 107 publications

(104 citation statements)

References 28 publications

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“…Brooks and Wiley, 1986;Wicken, 1980) or which find quantities analogous to entropy that increase during deterministic evolution (e.g. Ginzburg, 1977;Bomze, 1991;Demetrius, 1997;Baake and Wagner, 2001;Saakian et al, 2006;Wilson, 2008). However, a close analogy can be made when we consider evolution as a stochastic process: classical thermodynamics is based on the aggregate behaviour of a large number of molecules, just as population genetics depends on the aggregate behaviour of many reproducing genes.…”

Section: Accepted Manuscriptmentioning

confidence: 99%

On the application of statistical physics to evolutionary biology

Barton

Coe

2009

Journal of Theoretical Biology

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Section: Accepted Manuscriptmentioning

confidence: 99%

On the application of statistical physics to evolutionary biology

Barton

Coe

2009

Journal of Theoretical Biology

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“…In fact, Wilson developed this concept of rapidly generated retail centres well before Garreau produced his commentary, for Wilson's work was very much related to how one built supply-side dynamics into retail models [25,26]. All we can do here is give a sketch of how he proceeded.…”

Section: From Catastrophe and Bifurcation To Chaosmentioning

confidence: 99%

Cities in Disequilibrium

Batty

2017

Understanding Complex Systems

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Our perceptions of cities until quite recently were that they were largely stable in spatial structure over long periods of time, decades, even centuries, and that this suggested that they were in equilibrium. Cities appeared similar from generation to generation and although there were superficial changes due to fashion and technology, their overall structures were unchanging. To a large extent, this view of cities in equilibrium is borne of thinking about them physically but as soon as we unpack their dynamics, we realise that this a superficial perception. Cities are always in disequilibrium. They are in fact far-from-equilibrium being maintained through a tension of many countervailing forces that break down and build up on many different spatial and temporal scales, thus all coalescing in strong volatility and heterogeneity in urban form and function. Here we first review the concept of equilibrium and dynamics, and then we introduce ideas about discontinuity drawing on ideas from catastrophe and chaos theory. We argue that we should think of cities as being far-from-equilibrium structures and allude to ideas about innovation and technological change that condition their dynamic entirely. Our conclusion is that what happens in cities is increasingly disconnected from their physical form and this is particularly the case in the contemporary world where changes to the built environment are ever out-of-sync with changes in human behaviours, activity locations, patterns of movement, and globalisation.

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“…The problem, it seems to me, lies in restricting the measurement of flows to arbitrarily-defined sources and destinations that do not necessarily reflect the manner of organizational differentiation within natural systems. Wilson [1] and Wilson et al [2] papers address this issue.…”

Section: Introductionmentioning

confidence: 99%

‘In’ or ‘as’ space?: a model of complexity, with philosophical, simulatory, and empirical ramifications

Smith

2016

Complex Systems

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A General Systems model based on ideas originating with the writings of Benedict de Spinoza is described, starting with its philosophical underpinnings, and proceeding on to its relation to modern systems concepts, including attempts to simulate the relationships posed, and measure real world structures. Central to the idea is the notion that spatial extension may not have a prior existence, but emerges only through an entropy maximization process in which information and energy exchange is balanced among some limited number of subsystems that in sum comprise any given functioning complex system. Related published empiricism concerning geographical/geological systems -the hypsometry of stream basins, and overall internal zonation properties of earth structure -is briefly described; the former, especially, reveals a hierarchical pattern of potential energy relations that seems to well fit the organizational hypothesis. Possible applications of the model to genomic codon and medical imaging modeling are alluded to. A brief treatment of the relation of the model to basic properties of complex systems (connectivity, autonomy, emergence, etc.) is provided.

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Boltzmann, Lotka and Volterra and spatial structural evolution: an integrated methodology for some dynamical systems

Cited by 107 publications

References 28 publications

On the application of statistical physics to evolutionary biology

On the application of statistical physics to evolutionary biology

Cities in Disequilibrium

‘In’ or ‘as’ space?: a model of complexity, with philosophical, simulatory, and empirical ramifications

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