We address the dynamic of an energy price model in a more general approach; to our knowledge, in previous works, different conditions are imposed on the energy price function at a particular value in order to characterize stability and unstability for real or complex eigenvalues. Nonexistence of periodic orbits is shown by means of Dulac’s criterion; we also exhibit some pictures of solutions. Finally we modify this model and apply it to some particular cases in Venezuela economy. 1. Introduction Energy is a kind of natural resource that can be utilized to obtain power by mankind. It is an important basic resource for human survival, economical development, and social progress. It plays an important role in both the social and economic development and the structure of modernization. It is also an important lever in guiding and promoting the rational development, effective utilization, and optimal allocation of energy resources [1]. In the case of crude oil it is a key commodity for global economy. As a matter of fact, it is a vital component for the economic development and growth for industrialized and developing countries in a likely manner. Moreover, political events, extreme weather, and speculation in financial market, amongst others, are major characteristics of crude oil market which increase the level of price volatility in the oil markets. The effect of oil price fluctuation extends to reach large number of goods and services which have direct impact on the economy as well as the communities. Therefore, to reduce the negative impact of the price fluctuations, it is very important to forecast the price direction. Unfortunately, fundamental variables such as oil supply, demand inventory, and gross domestic product (GDP) are not available on daily frequency which adds additional difficultly to the prediction. Some studies have indicated that the global demand will continue to rise for the long term despite the fact that oil demands from Organization for Economic Cooperative Development (OECD) countries have decreased. However, the overall demand for oil has increased and this to a large extent is due to the increasing demands of non-OECD countries, especially China. The recent surge in the price of oil has created concern in both theory and practice. The reasons for this development can be premised on the following theoretical grounds: (i) oil price data are available at a high frequency and, therefore, there is increasing evidence of the presence of statistically significant correlations between observations that are large distance apart and (ii)
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