Dynamical Systems and Limit Cycles for Modelling Sustainable Agriculture and Cooperation

Concern about sustaining agriculture stems from the growing realization that deficiencies in meeting the social, economic and ecospheric purposes of agriculture may jeopardize its role in provisioning future generations of humans. The problem arises within the complexity of the agricultural system. This complex human system is difficult to model using the strong causality principle so successfully applied to disciplinary parts of the system. Almost twenty years ago, Samuelson addressed this issue with modifications to the Lotka Voltera predator-prey model. More recently, Mandelbrot's discovery of fractal geometry and independent work on the persistence and stability behaviour of nonlinear dynamical systems have generated new hope for modelling the holism of complex systems. This paper examines these developments in the context of sustainable agriculture and the role of cooperative processes. Sustainability emerges as a matter of seeking flexibility and solving problems at the boundaries of systems rather than seeking the correct trajectory or arriving at an equilibrium. The conclusions are that sustention of agriculture is a purpose-related concept, that the domain of attraction about an equilibrium is more important than the equilibrium itself, and that the bifurcation and adjoining of sets of trajectories of system variables at system boundaries is at the centre of development processes for sustainable agriculture and cooperation.

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Staff Paper

 Record created 2017-04-01, last modified 2017-08-29

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