Conditions on the Energy Market Diversification from Adaptive Dynamics

We study a mathematical model based on ordinary differential equations to describe the dynamic interaction in the market of two types of energy called standard and innovative. The model consists of an adaptation of the generalized Lotka-Volterra system in which the parameters are assumed to depend on a quantitative and continuous attribute characteristic of energy generation. Using the analysis of the model the fitness function for the innovative energy is determined, from which conditions of invasion can be established in a market dominated by the conventional power. The canonical equation of the adaptive dynamics is studied to know the long-term behavior of the characteristic attribute and its impact on the market. Then we establish conditions under which evolutionary ramifications occur, that is to say, the requirements of coexistence and divergence of the characteristic attributes, whose occurrence leads to the origin of diversity in the energy market.