A dynamical economic model of sustainable agriculture and the ecosphere

摘要

This paper addresses relationships between structural parameters of a complex three-dimensional system and agricultural wealth subject to a minimum safe standard for the ecosphere. The subsystems are the ecosphere, agriculture, and industry. Their interaction is modeled by a dynamical system based on the predator prey paradigm. It is demonstrated that the system may surpass certain local and global bifurcations. The later ones lead to appearance and disappearance of strange attractors.The presence of strange attractors connotes poor predictability. Sustaining agricultural systems requires the ability to predict departures from preferred reference states and in the limit to predict approaching extinction. A suitable model needs to be heuristic. Such a model should provide several features for managers and policy makers. It should incorporate learning about the minimum sustainable ecospheric threshold, preferred reference states, and the dynamics of departures from those reference states. Predictions of the model should reveal how to maneuver parameters in order to achieve ‘favorable’ system dynamics. That is why most of our attention is placed on exploring the range of parameters in which strange attractors occur or do not occur. The policy problem for sustainable agriculture is consequently defined as preventing strange attractors from appearing.Simulations show that strange attractors may be avoided and replaced by stable periodic trajectories or stable nodes by changing the coefficient of ecospheric recovery, terms of trade, or the productivity of the ecosphere in agricultural uses. Agricultural terms of trade and ecospheric recovery coefficients are partially substitutable in sustaining agriculture and improving predictability.The results suggest that sustainability is sensitive to learning processes which address tradeoffs among the parameters, minimum thresholds of persistence for the ecosphere and mutualism in economic predation.