Switching in heteroclinic networks

We study the dynamics near heteroclinic networks for which all eigenvalues of the linearization at the equilibria are real. A common connection and an assumption on the geometry of its incoming and outgoing directions exclude even the weakest forms of switching (i.e. along this connection). The form of the global transition maps, and thus the type of the heteroclinic cycle, plays a crucial role in this. We look at two examples in $\mathbb{R}^5$, the House and Bowtie networks, to illustrate complex dynamics that may occur when either of these conditions is broken. For the House network, there is switching along the common connection, while for the Bowtie network we find switching along a cycle

Almost complete and equable heteroclinic networks

Heteroclinic connections are trajectories that link invariant sets for an autonomous dynamical flow: these connections can robustly form networks between equilibria, for systems with flow-invariant spaces. In this paper we examine the relation between the heteroclinic network as a flow-invariant set and directed graphs of possible connections between nodes. We consider realizations of a large class of transitive digraphs as robust heteroclinic networks and show that although robust realizations are typically not complete (i.e. not all unstable manifolds of nodes are part of the network), they can be almost complete (i.e. complete up to a set of zero measure within the unstable manifold) and equable (i.e. all sets of connections from a node have the same dimension). We show there are almost complete and equable realizations that can be closed by adding a number of extra nodes and connections. We discuss some examples and describe a sense in which an equable almost complete network embedding is an optimal description of stochastically perturbed motion on the network

Past expectations as a determinant of equilibrium prices - hysteresis in a simple economy

We give an illustration of hysteresis (path-dependence) in a simple economy. In the presence of multiple possible equilibrium prices, we find that past expectations determine present prices. This phenomenon of path-dependence is robust under perturbations of the economy.Hysteresis, Path-dependence, Tatônnement, Equilibrium selection

Public Firms in a Dynamic Third Market Model

We set the third market model in a dynamic context to decide whether a country can achieve benefits by subsidizing a public rm's exports. We use calculus of variations with the constraint that the welfare is either maximized or grows at constant rate, reflecting the public concern of the firm. We conclude that a subsidy can be a good strategy for the country in some instances, even though only over a finite period of time. The duration of this period depends on the output strategy of the public firm as well as on exogenous factors.public firms, strategic trade policy, third market model, calculus of variations

Two generations sharing Adult Training (EFA) Courses - the impact of EFA certification on Lusophone immigrants and their descendants

This paper is part of my on ongoing PhD research entitled “Lives recounted – the impact of the EFA experience on the life trajectories of Lusophone labour migrants and their descendants”. My proposal in this paper is to explain the path that led me to introduce the issue of intergenerational relationships into my PhD research. Initially, the goal was to understand the impact of EFA certification2 on Lusophone immigrants’ lives. According to the official statistics, it is immigrants who rely most on EFA training courses. However, the first biographical interviews that I carried out showed that the category ‘foreign’ includes not only immigrants but also the descendants of immigrants who, for family or legal reasons, do not have Portuguese nationality. Many immigrant descendants, in fact, have difficulty in acquiring citizenship, which affects various dimensions of their lives, including access to and continuation in the educational system and labour market. In the official statistics these immigrants and their descendants appear in the category ‘foreigners’, i.e. despite being born in Portugal, a significant number of the descendants of immigrants have never been able to acquire Portuguese nationality. The situation found in the fieldwork has thus led to the resizing of the sample, which now considers not only Lusophone immigrants but also the descendants of Lusophone immigrants as a key object of analysis. I aim to understand the different impacts of EFA certification on their lives, treating the generational differences as a crucial point of analysis. Despite these two generations sharing the certification processes, I start from the assumption that the discourses on the impact of the EFA experience in their lives can be differentiated. In this paper I intend to show that the official statistics in the ‘foreign’ category embrace different groups and different generations, which appear interchangeably in a single category. On the basis of interviews conducted to date, I argue that being a Lusophone immigrants and the descendants of Lusophone immigrants form two distinct categories – for we are referring here to different generations that, despite the firmly established relationships between them, ultimately (self)evaluate the EFA experience differently

Art as a Cure: Analyzing Healthcare Treatment for the Mentally Ill through the Lens of Art Therapy Programs in Dakar, Senegal

Mental illness is a malady that affects roughly 2.3 million people in Senegal ( Statistics by Country” 2012), but the wide and sometimes opposing range of healing practices suggests that the attitudes surrounding mental illness are still largely contested. This is especially true in Senegal’s capital, where advances in medicine in big city hospitals are growing while ties to traditional beliefs and practices remain strong. Alternative therapies, such as art therapy, provide an opportunity for practitioners to explore different techniques for treating the mentally ill while still integrating elements of the local culture. It is precisely this integration that this paper aims to study, along with how art therapy works within the African context in order to be beneficial for its patients. With the information provided by both the artists that lead art therapy workshops, and the psychologists that supervise them, this paper will highlight the importance of cultural context when structuring healthcare programs for the mentally ill, since the beliefs that are deeply rooted in Senegalese tradition impact the entire way in which Senegalese citizens understand and respond to mental illness