A new transformation of parameters for generic discrete-time dynamical systems with two independent parameters is defined, for when the degeneracy occurs. Here the classical transformation of parameters (α1,α2)→(β1,β2) is not longer regular at (0,0); therefore, implicit function theorem (IFT) cannot be applied around the origin, and a new transformation is necessary. The approach in this article to a case of Chenciner bifurcation is theoretical, but it can provide an answer for a number of applications of dynamical systems. We studied the bifurcation scenario and found out that, by this transformation, four different bifurcation diagrams are obtained, and the non-degenerate Chenciner bifurcation can be described by two bifurcation diagrams.

Sustainable economic development requires ensuring economic growth and development in terms of environmental protection by providing a bridge between sustainable economic growth, improvement in human health, social justice, employment and environmental protection. Our paper aims to study the situation of green jobs at the European Union level and the relationship between environment and employment, by analysing the link between employment and environmental policies. It highlights the main trends recorded at the European Union level in the field of employment policy to promote green jobs for sustainable economic development. Although there is little effect from environmental policies on employment, the effects are positive, which shows that the relationship between environmental and employment policy should be continued and improved by measures taken at both the macro-and microeconomic levels. OPEN ACCESSSustainability 2015, 7 9232

This paper analyzes the impact of the COVID-19 pandemic on economic growth and electricity consumption and investigates the hypothesis of the influence of this consumption on the gross domestic product (GDP) for Romania. Using time series on monthly electricity consumption and quarterly GDP and a multi-linear regression model, we performed an analysis of the evolution of these indicators for 2007–2020, a comparison between their behavior during the financial crisis vs. COVID-19 crisis, and empirically explore the relationships between GDP and electricity consumption or some of its components. The results of the analysis confirm that the shock of declining activity due to the COVID-19 pandemic had a severe negative impact on electric energy consumption and GDP in the first half of 2020, followed by a slight recovery. By using a linear regression model, long-term relationships between GDP and domestic and non-household electricity consumptions were found. The empirically estimated elasticity coefficients confirm the more important impact of non-household electricity consumption on GDP compared to the one of domestic electricity consumption. In the context of the COVID-19 pandemic, the results of the study could be useful for optimizing energy and economic growth policies at the national and European levels.

Chenciner bifurcation appears for some two-dimensional systems with discrete time having two independent variables. Investigated here is a special case of degeneration where the implicit function theorem cannot be used around the origin, so a new approach is necessary. In this scenario, there are many more bifurcation diagrams than in the two non-degenerated cases. Several numerical simulations are presented.

No abstract