STUDYING THE INTERCONNECTION OF FOOD, ENERGY AND WATER RESOURCES USING THE THREE-SECTORAL LORENTZ MODEL

Abstract

The work is devoted to the problem of creating new methods for complex modeling and risk management, which will allow to study synergistic interactions between sources of risks of various origins under conditions of uncertainty. The paper proposes an approach to the study of the relationship between food, water and energy resources using the three-sectoral Lorenz model, combining in a single structure similarly described sectors of the economy, each of which is considered in terms of the productivity level, the workplaces number and the structural disturbances level. As a mathematical modeling result, the conditions of the deterministic chaos origin in the minimum economic development model were determined and possible reasons of the global economy growing vulnerability to small changes in management parameters were identified. The problem of determining effective controls for minimizing the total structural violations on selected time interval is considered. As a result of model experiments, the trajectories of control parameters changes were determined, which make it possible to reduce the structural violations number. This is achieved through changes in the ratio of supply and demand levels for products, demand and supply for workplaces creation. The influence of random perturbations on the deterministic attractors stochastic deformation of the Lorentz model is considered. It is shown that, under random perturbations, the trajectories of the stochastic system leave a deterministic attractor and form around it a certain bundle with the corresponding probabilistic distribution. The further model complicating possibility by taking into account other sectors of the economy using the Lorenz model in a complex form is considered. In this case the task of studying n sectors of economy is reduced to considering the behavior of an ensemble of n coupled oscillators that generate oscillations with frequencies ωn, respectively. Collective synchronization of oscillator data can be investigated using Kuramoto’s model. The problem of managing socio-economic development under the chaotic modes origin conditions is reduced for a complex model to controlling the frequency of a nonzero mean field generated by coupled oscillators.