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.