EQUILIBRIA AND DYNAMICS IN AN ECONOMIC PREDATOR-PREY MODEL OF AGRICULTURE

Long run trajectories for the shares of agricultural, industrial and ecospheric wealth in open interacting economic system are modelled by a three-dimensional system of ordinary differential equations using a predator-prey paradigm. For the two-dimensional case, corresponding to an ecosphere in equilibrium, stability properties are determined and possible bifurcation behaviour is described and interpreted. Bifurcation values for the parameters are described for the cases of less developed and industrialized economies. Discovery of rich dynamics, including the possibilities of bifurcations leading to creation of new attractors, offer promise that this modelling approach may shed greater light on the conditions under which economies may move to more desired levels of agricultural wealth. The model predicts that an agricultural economy ages by slowing its learning, seeking and obtaining greater stability, eventually leading to trapping. Efforts external to an economic system, such as freer trade or foreign aid require complementary endogenous restructuring of parameters to avoid regression to stable nodes or foci, or to limit cycles. Economic restructuring needs to focus on enriching the dynamics of system behaviour.