Nonextensivity at the edge of chaos of a new universality class of one-dimensional unimodal dissipative maps

We introduce a new universality class of one-dimensional unimodal dissipative maps. The new family, from now on referred to as the ($z_1,z_2$)-{\it logarithmic map}, corresponds to a generalization of the $z$-logistic map. The Feigenbaum-like constants of these maps are determined. It has been recently shown that the probability density of sums of iterates at the edge of chaos of the $z$-logistic map is numerically consistent with a $q$-Gaussian, the distribution which, under appropriate constraints, optimizes the nonadditive entropy $S_q$. We focus here on the presently generalized maps to check whether they constitute a new universality class with regard to $q$-Gaussian attractor distributions. We also study the generalized $q$-entropy production per unit time on the new unimodal dissipative maps, both for strong and weak chaotic cases. The $q$-sensitivity indices are obtained as well. Our results are, like those for the $z$-logistic maps, numerically compatible with the $q$-generalization of a Pesin-like identity for ensemble averages.Comment: 17 pages, 10 figures. To appear in European Physical Journal

On the Modelling of Price Effects in the Diffusion of Optional Contingent Products

In this chapter, we study the pricing strategies of firms in a multi-product diffusion model where we use a new formalization of the price effects. More particularly, we introduce the impact of prices on one of the factors that affect the diffusion of new products: the innovation coefficient. By doing so, we relax one of the hypotheses in the existing literature stating that this rate is constant. In order to assess the impact of this functional form on the pricing policies of firms selling optional contingent products, we use our model to study two scenarios already investigated in the multiplicative form model suggested by Mahajan and Muller (1991) (M&M). We follow a ‘logical experimentation’ perspective by computing and com- paring the results of three models: (i) The M&M model, (ii) a modified version of M&M where the planning horizon is infinite, and (iii) our model, where the new formalization of the innovation effect is introduced. This perspective allows us to attribute the differences in results to either the length of the planning horizon, or to our model’s formalization. Besides its contribution to the literature on pricing and diffusion, this paper highlights the sensitiv- ity of results to the hypothesis used in product diffusion modelling and could explain the mixed results obtained in the empirical validations of diffusion models (Mesak, 1996).MINECO under projects ECO2014-52343-P and ECO2017-82227-P (AEI) and by Junta de Castilla y León VA024P17 and VA105G18 co-financed by FEDER funds (EU)

The holm oak Myrto communis-Quercetum rotundifoliae in Alentejo - Portugal. Post-fire vegetation recovery in two stations (Forest Perimeter of Contenda and Aljustrel)

Abstract This work, developed in the Southern mainland Portugal, Alentejo, focused in the Forest Perimeter of Contenda (38º 01’ N e 7º 13’ W) and Aljustrel (37º 53’ N e 08º 07’ W), where holm oak forests belonging to the Myrto communis-Quercetum rotundifoliae Rivas Goday in Rivas Goday, Borja, Esteve, Galiano, Rigual & Rivas-Martínez 1960 have been identified. The Forest Perimeter of Contenda is subjected to the Forest Regime. Here, the field surveys were carried in an area destined to the maintenance of a healthy population of deer for hunting by means of sustainable management activities with minimal impacts on the ecosystem. In Aljustrel, the study area is not significantly disturbed by forestry or agricultural activities, so it has been maintained as a refuge for small game hunting species

Offensive and Defensive Marketing in Spatial Competition

While it is well-established that travel costs impact on customer preference toward local service providers, research about how this situation affects competitive marketing strategies remains sparse. This paper investigates, in a local market with two competing service providers, whether service providers should undertake defensive marketing, targeted at the nearest customers who typically prefer their offering for convenience and/or offensive marketing, directed to relatively remote customers who favor the rival as the closest alternative. We find that the service providers can exclusively undertake either defensive marketing or offensive marketing or combine the two in a full differentiated strategy at the equilibrium. We compare the outcomes of these three strategic options to identify the conditions under which they are worth implementing. Main findings suggest that service providers are better off undertaking offensive marketing alone when their rival’s retaliatory offensive capacity is weak and customers incur small travel costs. Otherwise, service providers may exclusively undertake defensive marketing or combine it with offensive marketing when travel costs become significant. Also, service providers should not invest in any marketing activity when they have no market power, like in the case of two adjacent outlets in a mall. Finally, the implications of these findings are discussed.MEC under projects ECO2014-52343-P and ECO2017-82227-P (AEI) and by Junta de Castilla y León under projects VA024P17 and VA105G18, co-financed by FEDER fund

Non-linear incentive equilibrium strategies for a transboundary pollution differential game

Producción CientíficaIn this paper we apply non-linear incentive strategies to sustain over time an agreement. We illustrate the use of these strategies in a linear-quadratic transboundary pollution differential game. The incentive strategies are constructed in such a way that in the long run the pollution stock (the state variable) is close to the steady state of the pollution stock under the cooperative mode of play. The non-linear incentive functions depend on the emission rates (control variables) of both players and on the current value of the pollution stock. The credibility of the incentive equilibrium strategies is analyzed and the performance of open-loop and feedback incentive strategies is compared in their role of helping to sustain an agreement over time. We present numerical experiments to illustrate the results.This research is partially supported by MINECO under projects MTM2016-78995-P (AEI) and ECO2014-52343-P and ECO2017-82227-P (AEI) and by Junta de Castilla y León VA024P17 and VA105G18 co-financed by FEDER funds (EU

Syntaxonomical checklist of Forest Perimeter of Contenda (Low Alentejo) – Portugal

Abstract The Forester Perimeter of Contenda (38 º 01 'N and 7 º 13' W) located in the Sierra Morena extreme west, limited on the east and south by the border between Portugal and Spain and north and west by the Arroyo, Murtigão and Pais Joanes streams. It has a total area of 5270.5ha, divided into three distinct areas: North Contenda, Intermediate Zone and South Contenda, subject to the Forest Regime. It belongs to the Santo Aleixo da Restauração parish, Moura municipality, Beja district and Alentejo province