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

Technology and Structural Change in Alberta Cereal Agriculture

Structural change and technology within the agriculture and food system in Alberta are becoming more complex as agriculture industrializes. This relationship is neither simultaneous nor unique according to work done on commercial cereal farms in central Alberta. The nature of the relationship appears to be one of periodic reversal of causality. Technology, characterised mainly as mechanical and chemical, shaped structure during the period represented by the 1971 census. Biotechnology is beginning now to have its own effect on fixed factor proportions distinct from that of mechanical technology. Mechanical technology change is having a greater effect on capital/labor ratios in 1986 than in 1971. Fixed factor proportions, as observed in 1986, appear to be becoming limiting to technology. Disturbances to the economic structure of agriculture by technological change normally bring reaction to preserve the status quo. The reaction, taking the form of subsidies and credit policies, may be counter productive to technological change required for competition in world markets during periods when structure determines technology. Perhaps the most important of these structural changes has been the declining rural equity in farm businesses which is slowly changing the self employed nature of agriculture to that of the owner/employee organisation of urban economies. This change makes farm family income increasingly dependent on off farm employment in rural and periurban areas. The results from this study lead to the conclusion that government policies to limit the consolidation of farms are more inhibiting now to technological change than they used to be. With the emergence of interest in agricultural free trade, it is more essential than ever before to distinguish between subsidies which compensate for hurt from hostile weather or foreign domestic policies, from those subsidies which address structural hurt from technological progress

Imapcts of Recovery Rates and Terms of Trade on Strange Attractors and Predictability in Sustainable Agriculture

Sustaining agricultural systems requires the ability to predict approaching extinction. Thus a suitable model needs to generate predictability as an intrinsic attribute. Such a model should provide several featuers for managerse. It should incorporate learning about the minimum sustainable ecospheric threshold. The model requires a capability to cope with uneven system coevolution. Solutions should reveal how to maneuver parameters to achieve'favourable' system dynamics. Models based on assumptions of lienarity and randomness are not able to explain sharp changes in system behaviour and do not result in predictability. Fortunately, theories for complex nonlinear dynamical systems are emerging from mathematics and physics in applications such as ecology, economics and immunology. This paper addresses the relationships between the structural parameters of a complex three-dimensional system and the predictability of wealth and sustainability. The subsystems are agriculture, the ecosphere and industry. Their interaction is modelled by a dynamical system based on the rpedator prey paradigm. The ecosphere is considered as a living interactive system that can regenerate, reproduce and become extinct. The model explores the dynamics of the whole system as the strucutral properties of its parts coevolve over time. We demonstrate that the structural parameters may pass through bifurcation values, which not only result in new equilibria and periodic trajectories, but account for the presence of strange attractors. Most of our attention is place on exploring the conditions under which strange attractors appear and dissappear in coevolution. The presence of strange attractors connotes great uncertainty and severely limits predictability. The policy problem for sustainable agriculture is to prevent strange attractors from appearing. The results are that agricultural terms of trade and ecospheric recovery rates are partially substitutable in sustaining agriculture. Strange attractors may be avoided and replaced by predictable periodic trajectories or stable node type equilibria by equilibria by changing the rate of ecospheric recovery, or terms of trade or the productivity of the ecosphere in agricultural uses. Portraits of the trasjectories are provided to make it easier to understand the dynamics. The results suggest that sustainability is sensitive to learning processes which address these tradeoffs, the approach to minimum thresholds of persistence for the ecosphere and the mutualism in economic predation. It may be ntoed that farmers historically learned about these things through artisan apprenticeship. Just as this learning method has been replaced by social, biological and physical sciences to achieve remarkable productivity gains, so resources need to be shifted to address the co-requisite ecospheric recovery processes