CONCEPTUAL MODELING OF EMERGENT PROCESSES IN DYNAMIC COMPLEX SYSTEMS NELSON FERNÁNDEZ 1-2 , JOSÉ AGUILAR 2 , OSWALDO TERÁN 3 1 Centro de Investigaciones en Hidroinformática, Universidad de Pamplona, Km 1 vía Bucaramanga. Pamplona. Colombia. nfernandez@unipamplona.edu.co / http://unipamplona.academia.edu/NelsonFernandez 2 Centro de Microelectrónica y Sistemas Distribuidos-CEMISID. Universidad de los Andes. Mérida. Venezuela. Aguilar@ula.ve 3 Centro de Simulación y Modelos-CESIMO. Universidad de los Andes. Mérida. Venezuela. oteran@ula.ve Abstract: - The proper study of Dynamical Systems (DS) considers phenomenal dynamics, from which it is possible to reach an approximate description of its operation and an explanation for their behavior, often complex and unpredictable. Studying dynamic systems (DSs) currently requires an integrated framework of concepts, which should allow analysis from a broader perspective. In response, this work expands the vision of Dynamic System (DS) from its complexity way and from the related dimensions of its Self-organization and Emergence, in addition with Homeostasis, and Autopoiesis dimensions (SEHA approach). Thus, in this document, firstly, DS is described and supported on the basis of its SEHA and, secondly, develops notions for each of the SEHA phenomena, which are described in detail based on its integration to a concept map model that facilitates the observation of their relations, especially regarding DS self-organization. This approach is a synergic and promising way to understand processes and mechanisms that govern surrounding or constructed DS-SEHA, at the time it sets up the bases for a future formalization with modeling aims. Key-Words: - Complexity, Self-organization, Homeostasis, Autopoiesis, Emergence, Conceptual Map, Dynamical System’s Structure. 1 Introduction Dynamic systems raise great interest due to their variety and cosmopolitan existence in the physical universe as well as in the laws universe that supports much of the sciences created by humanity. The basic trait of any DS is the change of state in time, according to a law governing its evolution [1]. From this start point, in DSs with a large set of components, the presence of other peculiarities has been observed, including high interconnection level, mutual interdependence, role plasticity and adaptability, and pattern generation, among others [2]. Based on these characteristics and the autonomous behavior of its elements, DSs can accomplish tasks with considerable difficulty. This is possible, as rules evolving from simple to complex and being independent from any superior level instruction or central control, direct its elements. Such condition determines DS capacity to establish its own organization based on a self-organization process that has at the same time, as a common factor, the emergent dimension of its global order and behavior [3]. Starting from the self-organization and emergence processes, the particular fact of difficulty to explain the global order and behavior of DS based on the interactions of its individual elements arises [4]. This event, which defines the DS complexity, translates into modeling terms, as the property that challenges formulation of complete order and behavior of the system in a given language, even when reasonably complete information on its atomic components and interactions is available [5]. In other words, DS complexity relies on the difficulty of explaining and modeling emergent properties based on the system’s self-organization. This situation turns equally complex when pretending to explain and modeling self-organization from the emergencies. Although self-organization and emergence have been the basis of a promising approach in different fields (e. g. self-organization engineer, multiagent systems and adaptive complex systems [6]), it becomes necessary to expand the study to inherent and complementary phenomena, which at the same time support those basic features, such as the ones related to adaptability and autonomy. These are situations that favored the maintenance of the system structure Advances in Computational Intelligence, Man-Machine Systems and Cybernetics ISBN: 978-960-474-257-8 75