Dynamics of a minimal consumer network with bi -directional influence

Fashion cycle dynamics induced by agents' heterogeneity for generic bell-shaped attractiveness functions

“…We recall that in [40,Subsection III.A] also the scenarios with V = 0.2 and V = 0.5 were investigated. However, since in those frameworks only transcritical bifurcations of a = 0 and a = 1 were detected, at which the two trivial equilibria switch from stability to instability or vice versa, and since the stability conditions found in Corollary 2.7 with respect to for a = 0 and a = 1 do not depend on the expression of A i , such scenarios remain exactly as in [40] for the Gaussian and parabolic formulations of attractiveness in (19) and (20). Thus we omit the corresponding analysis, focussing just on the third scenario considered in [40,Subsection III.A], in which V = 0.8.…”

“…Namely, we wish to highlight how the sociological and economic interpretation of the main scenarios provided in [40] cannot be precisely repeated in correspondence to the Gaussian formulation for attractiveness in (19), despite the resemblance in the dynamic outcomes which is apparent comparing Figure 5 in [40] with Figure 1(A). Before performing such interpretative task, let us now briefly investigate how the bifurcation analysis conducted dealing with the Gaussian map changes when considering the parabolic formulation for attractiveness in (20). Showing in Figure 5 the bifurcation diagram of g with f 2 as in (20), for ∈ (0, 0.9), at first we find a confirmation of the theoretical results in Section 2, which ensure that the same transcritical bifurcations as in Figure 1(A) and in Figure 5 in [40] occur at a = 0 and at a = 1, and that the number and value of the nontrivial equilibria coincide for any when different attractiveness functional forms are taken into account.…”

“…Before performing such interpretative task, let us now briefly investigate how the bifurcation analysis conducted dealing with the Gaussian map changes when considering the parabolic formulation for attractiveness in (20). Showing in Figure 5 the bifurcation diagram of g with f 2 as in (20), for ∈ (0, 0.9), at first we find a confirmation of the theoretical results in Section 2, which ensure that the same transcritical bifurcations as in Figure 1(A) and in Figure 5 in [40] occur at a = 0 and at a = 1, and that the number and value of the nontrivial equilibria coincide for any when different attractiveness functional forms are taken into account. Moreover, for the considered parameter configuration, a = a * 1 and a = a * 2 are still unstable when they lie in the interval (0, 1).…”

“…Finally, we stress that, rather than considering stable preferences as we do, it is possible to deal with preference adjusting consumers, like in [22][23][24][25][26]33], where cycles are found in a model with agents having globally interdependent preferences. The setting proposed in those works has been extended in [19,20], to deal with the case in which the interdependence among preferences is local in nature, and in [32], where the authors propose a stochastic version of the original framework. We recall that consumption choices of agents disposed on a network and having locally interdependent preferences have been considered in [10], too.…”

A Survey of Hydrogen Energy and I-Energy Applications: Household Intelligent Electrical Power Systems

“…Smart Meters (SMs) are chosen as potential devices in SGs. In this context, SM is a smart device that aims to measure smartly the energy consumption and helps users to get a report about their energy consumption [73]. Smart Grid Data Measurement includes infrastructure for coordinating and storing data for AMI applications, including a database for calculating data from smart meters to a Measurement Data Collection center (MDC).…”