Dynamical Systems and Limit Cycles for Modelling Sustainable Agriculture and Cooperation
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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.