Elements of a methodology to assess the alignment of core-values in collaborative networks

Collaborative networks are typically formed by heterogeneous and autonomous entities, and thus it is natural that each member has its own set of core-values. Since these values somehow drive the behaviour of the involved entities, the ability to quickly identify partners with compatible or common core-values represents an important element for the success of collaborative networks. However, tools to assess or measure the level of alignment of core-values are lacking. Since the concept of 'alignment' in this context is still ill-defined and shows a multifaceted nature, three perspectives are discussed. The first one uses a causal maps approach in order to capture, structure, and represent the influence relationships among core-values. This representation provides the basis to measure the alignment in terms of the structural similarity and influence among value systems. The second perspective considers the compatibility and incompatibility among core-values in order to define the alignment level. Under this perspective we propose a fuzzy inference system to estimate the alignment level, since this approach allows dealing with variables that are vaguely defined, and whose inter-relationships are difficult to define. Another advantage provided by this method is the possibility to incorporate expert human judgment in the definition of the alignment level. The last perspective uses a belief Bayesian network method, and was selected in order to assess the alignment level based on members' past behaviour. An example of application is presented where the details of each method are discussed.

Big bang bifurcations in von Bertalanffy’s dynamics with strong and weak Allee effects

The main purpose of this work was to study population dynamic discrete models in which the growth of the population is described by generalized von Bertalanffy's functions, with an adjustment or correction factor of polynomial type. The consideration of this correction factor is made with the aim to introduce the Allee effect. To the class of generalized von Bertalanffy's functions is identified and characterized subclasses of strong and weak Allee's functions and functions with no Allee effect. This classification is founded on the concepts of strong and weak Allee's effects to population growth rates associated. A complete description of the dynamic behavior is given, where we provide necessary conditions for the occurrence of unconditional and essential extinction types. The bifurcation structures of the parameter plane are analyzed regarding the evolution of the Allee limit with the aim to understand how the transition from strong Allee effect to no Allee effect, passing through the weak Allee effect, is realized. To generalized von Bertalanffy's functions with strong and weak Allee effects is identified an Allee's effect region, to which is associated the concepts of chaotic semistability curve and Allee's bifurcation point. We verified that under some sufficient conditions, generalized von Bertalanffy's functions have a particular bifurcation structure: the big bang bifurcations of the so-called box-within-a-box type. To this family of maps, the Allee bifurcation points and the big bang bifurcation points are characterized by the symmetric of Allee's limit and by a null intrinsic growth rate. The present paper is also a significant contribution in the framework of the big bang bifurcation analysis for continuous 1D maps and unveil their relationship with the explosion birth and the extinction phenomena.