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Esta obra responde a la necesidad de divulgar una forma de entender y analizar la sostenibilidad de los paisajes que incluya todas las categorías de usos agropecuarios, con el objetivo de que tenga un marco institucional propio. La concepción de sostenibilidad desarrollada en este libro se deriva de una construcción conceptual y metodológica, generada de manera concertada con instituciones de carácter nacional comprometidas con el desarrollo sostenible rural de Colombia.

Resumen: Se plantea una metodología para el modelado de la sostenibilidad empresarial basado en la dinámica de sistemas e integrando elementos del análisis matemático, estadístico y de los sistemas dinámicos. Para ello, se revisan los aspectos generales referentes al desarrollo sostenible. Entre estos, las características e indicadores relacionados con la empresa sostenible, los conceptos claves de la dinámica de sistemas, los sistemas dinámicos y el modelamiento de la sostenibilidad empresarial. Se detalla la metodología propuesta y luego se describe su aplicación al caso específico de una empresa manufacturera de carácter nacional. Mediante la construcción del modelo, su simulación y análisis se logra establecer acciones de sostenibilidad relacionadas con la gestión del talento humano, el ahorro energético y la generación de residuos sólidos. El modelo desarrollado permite a la empresa analizar diversas alternativas y observar si contribuyen a mejorar el desempeño de la empresa.

RESUMEN El proceso sancionatorio por infracción ambiental en Colombia incluye el ejercicio de tasación de multas (Ley 1333 de 2009), el cual tiene como metodología la establecida en la Resolución 2086 de 2010, propuesta por el Ministerio de Ambiente, Vivienda y Desarrollo Territorial (MAVDT) en el 2010. Sin embargo, a pesar que la metodología de tasación está aprobada y publicada, su implementación por parte de las diferentes instituciones públicas que ejercen como autoridad ambiental en el país no es expedita, debido fundamentalmente a que tal metodología contiene dejos en la escritura que no facilitan el entendimiento del procedimiento de tasación en apartados importantes. Este artículo tiene como objetivo fijar fundamentos conceptuales para la tasación de multas de acuerdo con la metodología aprobada en Colombia y presentar explícita y claramente cada una de las fórmulas con las que se debe realizar la tasación, de modo que el criterio de tasación entre el personal especializado se corresponda con la norma. La base de la discusión es ver la multa como la suma del beneficio ilícito y el daño ambiental, sea este último real o potencial. Se concluye que la fórmula de tasación de multas por infracción ambiental en Colombia es adecuada para los procesos sancionatorios que se desarrollan en el país. JEL: H23, O13, Q51, Q52. ABSTRACT The sanctioning process for environmental infringement in Colombia includes the exercise of determining fines (Law 1333 of 2009), with a methodology established in the Resolution 2086 of 2010, and proposed by the Ministry of Environment, Housing, and Territorial Development (MAVDT for its initials in Spanish) in 2010. Nevertheless, despite the fact that there exists an approved and published determination methodology, its implementation by different public institutions that exercise environmental authority in the country is not clear, mainly due to the fact that such methodology contains details in the writing that do not facilitate the understanding of the procedure in important sections. This article aims to establish conceptual foundations for the determination of fines according to the methodology approved in Colombia, as well as to present-in an explicit and clear manner-each formula that is necessary in the determination process, so that determination criteria used by specialized personnel match the standards. The basis of the discussion is to consider fine as the sum of illicit benefits and environmental damage, whether the latter is real or potential. The paper concludes that the formula for the determination of fines for environmental infringement in Colombia is adequate for the sanctioning processes that take place in the country. RESUMO O processo punitivo por infração ambiental na Colômbia inclui o exercício de estabelecimento de taxas de multas (Lei 1.333 de 2009), que tem como metodologia a estabelecida na Resolução 2.086 de 2010, proposta pelo Ministério de Ambiente, Habitação e Desenvolvimento em 2010. Contudo, embora a metodologia de taxação esteja aprovada e publicada, sua implantação por parte das diferentes instituições públicas que exercem como autoridade ambiental no país não é expedita, devido a que tal metodologia contém lacunas na escrita que não facilitam o entendimento do procedimento para estabelecer multas de acordo com a metodologia aprovada na Colômbia e apresentar explícita e claramente cada uma das fórmulas com as quais a taxação deve ser realizada, de modo que o critério de taxação entre o pessoal especializado corresponda com a norma. A base da discussão é ver a multa como a soma do benefício ilícito e do dano ambiental, seja este último real ou potencial. Conclui-se que a fórmula para estabelecer multas por infração ambiental no país é adequada para os processos punitivos nele desenvolvidos.

We present a hybrid algorithm based on Genetic Algorithms and Discrete Event Simulation that computes the algorithmic-optimal location of emergency resources. Parameters for the algorithm were obtained from computed historical statistics of the Bogotá Emergency Medical Services. Considerations taken into account are: (1) no more than a single resource is sent to an incident, (2) resources are selected according to incidentpriorities (3) distance from resource base to incident location is also considered for resource assignment and (4) all resources must be used equally. For every simulation, a different set of random incidents is generated so it’s possible to use the algorithm with an updated set of historical incidents. We found that the genetic algorithm converges so we can consider its solution as an optimal. With the algorithmic-optimal solution we found that arrival times are shorter than the historical ones. It’s also possible to compute the amount of required resources to reduce even more the arrival times. Since every Discrete Event Simulation takes a considerable amount of time the whole algorithm takes a heavy amount of time for large simulation time-periods and for many individuals for generation in the genetic algorithm, so an optimization approach is the next step in our research. Also, less restricted considerations must be taken into account for future developments in this topic.

This document shows a model that seeks the sustainability of the Usable Solid Waste (USW) market in Bogotá, based on System Dynamics (SD), in order to understand the complex behavior of the phenomena that should be presented in this city market in the context of sustainability. Dynamic hypothesis suggests that two negative feedback structures exits, one that represents demand and another that represents supply and that interact under the assumption of free market with government intervention. Different strategies were modeled on both the demand side and the supply side to manage the system. As conclusion, the linear way in which the USW market currently develops is not adequate. It is necessary to institutionalize the market using the price so that it contributes to its sustainability and that both demand and supply are encouraged at the same time. Besides, district policy oriented to supply must be in accordance with the national policy that encourages demand to use more USW. Likewise, the internalization by all the actors of the market and applicability of the norm is required. The creation of public-private partnerships is required for the development of innovative projects in this area. Resumo O presente documento mostra um modelo que busca a sustentabilidade do mercado de Resíduos Sólidos Utilizáveis (USW) em Bogotá, com base na Dinâmica de Sistemas (SD), para entender o comportamento complexo dos fenômenos que devem apresentar-se neste mercado de cidade no contexto da sustentabilidade. A hipótese dinâmica sugere que há duas estruturas de comentário negativo, uma que representa a demanda e o outra que representa a oferta, e que interage baixo à suposição de mercado livre com a intervenção do governo. Diferentes estratégias foram moldadas em ambos os lados, tanto demanda quanto oferta, para dirigir o sistema. Como conclusão, o caminho linear no qual o mercado USW atualmente se desenvolve, não é adequado. É necessário institucionalizar o mercado usando o preço de maneira que contribua para a sua sustentabilidade e que tanto a demanda como a oferta sejam estimuladas ao mesmo tempo. Além disso, a política de distrito orientada para o fornecimento, deve estar conformada à política nacional que estimula a exigência de usar mais USW. Do mesmo modo, é necessário que todos os atores do mercado internalizem e apliquem as normas. Também é necessária a criação de alianças entre os setores público e privado para o desenvolvimento de projetos inovadores nesta área.

This article builds and evaluates a business sustainability model for a manufacturing industry in which indicators of sustainable development are incorporated. The construction and analysis of the model is based on the system dynamics methodology. This methodology begins with the characterization of business sustainability and its indicators, models and applied methodologies are then reviewed, the production process of the analyzed company described, and the model is finally elaborated integrating the environmental, economic and social dimensions. The simulations of the model showed that the inventory of finished products accumulates over time and that the incorporation of energy saving technology is one that has a more effective impact on consumption, and the proportion of waste generated grows as the production order’s size increases. Finally, it is concluded that the designed model is useful for the evaluation of strategies and the definition of sustainability actions. Resumen En este artículo se construye y evalúa un modelo de sostenibilidad empresarial para una industria manufacturera en el cual se incorporan indicadores del desarrollo sostenible. La construcción y el análisis del modelo se basa en la metodología de dinámica de sistemas. En esta metodología se parte de la caracterización de la sostenibilidad empresarial y sus indicadores, se revisan modelos y metodologías aplicadas, se describe el proceso productivo de la empresa analizada y se elabora el modelo integrando las dimensiones ambiental, económica y social. Las simulaciones del modelo mostraron que el inventario de productos terminados se acumula a través del tiempo, la incorporación de tecnología de ahorro energético es la que tiene un impacto más efectivo en el consumo, y la proporción de residuos generados crece a medida que aumenta el tamaño de la orden de producción. Finalmente se concluye que, el modelo diseñado es útil para la evaluación de estrategias y definición de acciones de sostenibilidad.

En este artículo se presenta un modelo matemático y la evaluación de distintos escenarios de la estimación de la tendencia del consumo de agua en el proceso productivo del bioetanol en Colombia. El modelo fue establecido con la metodología de dinámica de sistemas, la cual permitió representar las principales variables de la cadena de producción de bioetanol y la vinculación del consumo de agua por hectárea y por litro de bioetanol producido. La información para la construcción, validación y calibración del modelo fue obtenida de la Federación Nacional de Biocombustibles. Se evaluaron estrategias técnicas para el ahorro de consumo de agua, y se evidenció que sin estas el consumo de agua seguirá en aumento, debido al incremento de producción en Colombia.

The regional integration of electricity markets has been established as desirable among the South American nations to meet demands through the possible consolidation of a unified competing market in the medium term (CAN, 2010). However, what remains to be defined are rules of the game with satisfactory benefits for all parties that have been demonstrated. In this paper we propose a model of power integration based on the Market Coupling scheme, which starts with the modeling of the national markets using the System Dynamics modeling methodology. As a result, the expected behavior of the system is obtained, except in the case of exports, in which, because of the assumption of an infinite transmission capacity between nations, it is seen to surpass the real values found in the market. The work presented in this document (based on two nations, Colombia and Ecuador) allows experimentation for the formulation of the rules of the game necessary in the regional integration of markets.

espanolIntroduccion: Las palomas (Columba livia) son parte cultural de los centros historicos de las grandes ciudades del mundo -entre ellos la Plaza de Bolivar de la ciudad de Bogota, Colombia-, sin embargo, son una especie invasora que puede llegar a ser una amenaza para la salud publica de los visitantes de la Plaza, razon por la cual es necesario controlar el incremento neto de estas aves sin buscar su extincion. Objetivo: En este trabajo se construyo un modelo matematico del crecimiento de la poblacion de palomas, bajo una serie de pulsos de control a traves del tiempo, para observar el comportamiento de desarrollo controlado de estas aves. Materiales y metodos: Como herramienta principal se utilizo la metodologia de modelamiento conocida como Dinamica de Sistemas, la cual permite obtener un sistema de ecuaciones diferenciales a partir de una representacion sistemica de un problema. Resultados: Los resultados indican que la simulacion de este tipo de control permite que la poblacion de palomas se mantenga dentro de un rango aceptable para el espacio. Conclusiones: Este trabajo se considera un gran aporte en la simulacion y evaluacion de escenarios para el control de poblacion de palomas, mediante la evaluacion con Dinamica de Sistemas y puede reproducirse para otras especies problema. EnglishIntroduction: The pigeons (Columba livia) are a cultural part of the historical centers of the great cities of the world; however, they are an invasive species that can become a threat to the public health of visitors to the Plaza de Bolivar in Bogota, which is why it is necessary to control the net increase of these birds, without seeking extinction. Objective: In this work a mathematical model of the population growth of pigeons was constructed, under a series of control pulses through time, to observe the behavior of controlled development of these birds. Materials and Methods: As a main tool we used the modeling methodology known as System Dynamics, which allows us to obtain a system of differential equations from a systemic representation of a problem. Results: The results indicate that the simulation of this type of control allows the population of pigeons to remain within an acceptable range for space. Conclusions: This work is considered a great contribution in the simulation and evaluation ofscenarios for the population control of pigeons, through the evaluation with Systems Dynamics and can be reproduced for other problem species. portuguesIntroducao: As pombos (Columba livia) sao parte cultural dos centros historicos das grandes cidades no mundo, incluindo a Praca Bolivar na cidade de Bogota, Colombia, no entanto, sao uma especie invasora que podem se tornar uma ameaca para a saude publica dos visitantes da Praca, e por isso que e necessario controlar o aumento liquido dessas aves sem buscar a extincao. Objetivo: Neste trabalho construiu-se um modelo matematico do crescimento da populacao de pombos, sob uma serie de pulsos de controle no tempo, para observar o comportamento de desenvolvimento controlado dessas aves. Materiais e metodos: Como ferramenta principal, utilizou-se a metodologia de modelagem conhecida como Dinâmica de Sistemas, que permite obter um sistema de equacoes diferenciais a partir de uma representacao sistemica de um problema. Resultados: Os resultados indicam que a simulacao deste tipo de controle permite que a populacao de pombos permaneca dentro de um intervalo aceitavel para o espaco. Conclusoes: Este trabalho e considerado uma grande contribuicao na simulacao e avaliacao de cenarios para o controle da populacao de pombos, atraves da avaliacao com a Dinâmica de Sistemas e pode se reproduzir para outras especies problema.

De acuerdo a referencias, existe una fuerte influencia del estrés con el desarrollo de enfermedades. En este trabajo se consideraron los atributos que hacen posible esa influencia para la elaboración de un modelo matemático que permite el planteamiento de escenarios que cambian con la frecuencia con la que un individuo implementa soluciones temporales para atender el estrés (pseudosoluciones) o cambia la frecuencia con la que recibe el tratamiento médico especializado para atender la enfermedad. Los resultados son concluyentes de la dinámica del comportamiento del sistema, permitiendo la configuración de escenarios en los que es posible que el paciente: 1) sane completamente, 2) alcance niveles estables de estrésenfermedad que puede sobrellevar sin riesgos pero con la implementación de diferentes pseudosoluciones y tratamientos médicos, o 3) ponga en riesgo su vida.

De acuerdo con lo presupuestado para 2019, se realizó la publicación en Journal of Physics indexado en Scopus Q3, de un artículo en el que se definen los métodos y modelos matemáticos para la representación de paisajes y sus indicadores de gobernanza, bienestar y sostenibilidad, para la posterior implementación de escenarios de intervención hacia la sostenibilidad del sistema socioecológico. El modelo matemático que se propone, debe construirse con la metodología de la Dinámica de Sistemas, para la obtención de un sistema de ecuaciones diferenciales ordinarias de primer orden en dependencia del tiempo, en el que se represente la compleja trama del sistema socioecológico del paisaje que se estudia, en términos de interdependencias, interacciones e interretroacciones de todas sus partes (sociales, ambientales, económicas, etc.). Se concluye que los análisis de sostenibilidad y los análisis de gobernanza no pueden ser representados con las mismas técnicas porque se representan objetos distintos, que la gobernanza debe ser analizada conjuntamente con la gobernabilidad, dado que no son lo mismo, y que el bienestar condiciona los análisis de sostenibilidad y los análisis de gobernanza y gobernabilidad. Bogotá Evaluación y Monitoreo de la Biodiversidad

Natural gas is considered the fuel of the transition of fossil sources and renewable energies. This is why demand levels have increased worldwide, which requires the intervention of public and private actors to meet these requirements. Participation in the supply of diverse interconnected actors of the provider-client form, a supply chain for natural gas, in which the effects of the application of the policies that can be analyzed in time, through the use of a Model Based on Systems Dynamics for the Colombian case. The results of the model show the behavior of reserve levels, production, and transport against the levels of implementation of the policies formulated by the national government, which allows recommending actions to decision makers in the planning of policies aimed at a guarantee the uninterrupted supply of this resource.

The purpose of this short-paper is to show an overview of academic research in business faculties, making emphasis on the way the interactions of project life cycle and product life cycle are the support for the improvement of organizational capabilities. We start by addressing the generalities of research systems; later, we get into some ideas about the management of research processes in business faculties; we exemplify the management of these kind of projects; and finally, we show the general way in which project life cycle and product life cycle support the improvement of organizational capabilities in business faculties.

This article presents preliminary results of the mathematical analysis of a national energy market. The modeling of the studied system was made from causal relationships between the supply and demand of a national energy market, obtaining a system of ordinary differential equations of the first order of the electric power capacity in construction, the electric power capacity installed and the price of electricity in the market (Redondo et.al, 2018). In the dynamic analysis of the model, a saddle-node bifurcation was identified for the case in which the elasticity of the price with respect to the reserve margin is considered null, which allowed establishing two prospective scenarios of the system: absolute disappearance of the supply of electricity or tendency of growth of the supply to the attention of the demand of the market

The biofuels industry has grown and has positioned itself in Colombia for national purposes, these come from biomass sources such as agricultural crops. Bioethanol is the most used in Colombia and is obtained from sugarcane. One of the main concerns of the sector and society, is the high water consumption associated with agricultural crops (9,000 m3 / ha-year), there are currently 232,000 hectares of sugarcane for the production of sugar and bioethanol. Given the aforementioned, the need arises to carry out a planning of industrial increase of the sector taking into account as a main base the demand and availability of water resources for different activities in the Cauca river basin and the demand for sugarcane crops. In this document it is presented a mathematical model and the evaluation of different scenarios of the estimation of the trend of water consumption in the bioethanol production process in Colombia and in this way to establish scenarios of high risk of water shortage both for the population, interested parties and cane cultivation.

Historical civilizations have evidenced different routes to the collapse mainly due to political, warfare, cultural and environmental damages. This has animated modern researches to study and understand social, economic, and environmental challenges that modern societies must adopt in order to avoid history from repeat itself, and even worst, irreversibly. Many of these researches are focused on modelling through sets of ordinary differential equations (ODE's) representing the dynamic interaction between natural resources and population in an isolated society. In this work, we introduce the fact of cooperation between two similar societies, modelled as sets of ODE's of the type Brander and Taylor (1998), in the sense that economical exchange can exist between them. We couple two societies by introducing a simple receive-and-protect rule in which one society receive the other's help under the condition of protecting its own resources. We set that this cooperation may be constant, when it does not change all over the time, or changes intermittently depending on the level of resources each society has at any time. When cooperation is constant, the resulting system is a 4-dimensional system of ODE's that evolves smoothly, but if cooperation is intermittent, the coupled 4-dimensional system becomes a Filippov system. In both cases, we found that under economic cooperation, societies can survive at least in the long run, different from what happens when both societies are treated in isolation for the same parameter values.

In this paper, we show the preliminary results in a proposed a model for the supply and demand of electricity in a domestic market based on system dynamics. Additionally, the model indicates piecewise smooth differential equations arising from the diagram of flows and levels, using dynamical systems theory for the study of the stability of the equilibrium points that have such a system. A bifurcation analysis approach is proposed to define and understand the complex behavior. Until now, no work has been reported related to this topic using bifurcations criteria. The growing interest in personal ways of self-generation using renewable sources can lead the national grid to a standstill and low investment in the system. However, it is essential to preserve the national network as a power supply support to domestic and enterprise demand. To understand this scenario, we include an analysis of zero-rate demand growth. Under this hypothesis, a none smooth bifurcation appears related to a policy which involves the variation of the capacity charge. As a first significant result, we found that it is possible to preserve the investments in the market since, through the capacity charge parameter, the system dynamics can be controlled. Then, from a business approach, it is necessary to know the effects of the capacity charge as the strategic policy in the system generation price scheme.

ONTARE. REVISTA DE INVESTIGACIÓN DE LA FACULTAD DE INGENIERÍA En este trabajo se presenta una metodología novedosa para la toma de decisiones basada en la dinámica del sistema y los sistemas dinámicos. Aquí se muestra cómo el diagrama de bifurcaciones es en realidad un mapa de todos los escenarios posibles. Esta herramienta es muy importante para los gerentes y los administradores públicos, porque el ejercicio de la toma de decisiones se torna más sencillo cuando la comprensión del problema se ve mejorada. En este documento mostraremos algunos alcances de esta metodología usando como ejemplo un modelo para la creación de empresas en una zona industrial.

Recent methods for sustainability analysis have involved the methodology of system dynamics for the representation of different landscape components that are analyzed. This document proposes a mathematical model based on system dynamics for the hydrological component in the sustainability analysis that includes the processes between precipitation and runoff. Additionally, the stability of the equilibrium point found with the theory of dynamic systems is studied. The modeling is carried out from a diagram of levels and flows, in order to obtain a system of ordinary differential equations of first order, linear, non smooth, that takes as state variables static and capillary storage, superficial storage, higher gravitational storage, lower gravitational storage (aquifer) and storage in the channel. The model was validated with time series of the Chinchina basin (Caldas, Colombia). From dynamical systems point of view, the system behavior has an equilibria point that depends on the saturation value in the static and capillary storage.

The effect of implementation of policies, programs, plans and projects on the social, economic and environmental aspects of landscapes responds to conditioning factors that give a degree of sensitivity to these landscapes. The objective of this paper is to propose a landscape analysis methodology that allows to identify guidelines and priorities for landscape management. We have called this methodology the implications networks and it is based on chains of cause-effect relationships, in which the direct, indirect and cumulative (additive or synergistic) implications of the different types of actions on landscapes are considered. This methodology has been used in Colombia to establish the socio-environmental sensitivity of landscapes to the plans for the expansion of electric transmission, nature tourism, the moving of hydrocarbons by pipelines and wagons, demonstrating their usefulness and relevance for making decisions in these sectors, as well as to analyze the incidence of land use policies in Andean landscapes. The experience gained from the implementation of the implications networks methodology allows us to conclude that this is a useful and versatile systemic analysis tool to conduct studies and establish guidelines for the integral management of territories with multiple landscape units and various socio-environmental conditions.

A mathematical model for international integration of national energy markets was proposed by references. Lowering the dimension conveniently to 3 dimensions using system dynamics methodology, the dynamical system obtained could present a commutation region proposing that the system is a piecewise smooth system PWS with local bifurcations: Saddle-node and transcritical bifurcations. The bifurcation diagram is interpreted as a map of all possible system prospective scenarios, in this sense, the making decisions over systems have leverage points in its bifurcation parameters. In the national energy markets case, the bifurcations parameters depend on the generation lifetime and the investments rate, then two trend scenarios were defined: the absolute disappearance of the national supply of electricity or convergency at an equilibrium value of the national supply with which it is possible to serve the market. It is concluded that any investment and small useful life of the generation plants is not enough for attending the national electricity demand in the medium and long term.

Sustainable development is a concept that has been maturing since its promulgation in Brundtland in 1987. Following a complex systems-based reflection that involves system dynamics, dynamical systems and viability theory, is proposed that sustainability is an emerging expression of the landscape, whose emergence results from the socio-ecological interactions of the landscape, so its analysis must be of a type systemic, incorporating the temporal transformation of all landscapes aspects, and not only portions of them, in addition, in this paper is explained that sustainability does not exist as a single state, but that there are sustainabilities and that, although its analysis is specific space, it should allow comparison with higher and lower spatial scales. In this way, a methodological approach is made from dynamical systems theory for sustainability landscape analysis. This perspective not only allows to recognize the trend behavior of a socio-ecological system in the landscape establishing its sustainability, but it is also oriented to decision-making, so, the management of sustainability indicators should not be done as if in the landscape were disconnected, causing possible deterioration of other indicators during the management, but through sustainability principles defined as indicators set satisfying constraints. In this way, the perspective from the dynamical systems theory allows the recognition of sustainability and guides on the decision making in the landscape.

Resumen Este artículo presenta un modelo para la evaluación de estrategias en la gestión de Residuos de Aparatos Eléctricos y Electrónicos (RAEE). Estos residuos representan un riesgo para la salud pública y para el medio ambiente, por los compuestos de tipo peligroso que los constituyen y el aumento de su generación. En Colombia existe desde 2013 la ley 1672 lineamientos para la adopción de una política que mejore la gestión de los RAEE. Esta Ley propone objetivos gestión pública, de los cuales en este artículo se evaluaron tres de ellos (Reducción en la generación, incentivo al aprovechamiento, promover la participación integrada). Para esta evaluación, se construyó un modelo utilizando la metodología de Dinámica de Sistemas, la cual permitió establecer la estructura del sistema socio-ambiental de generación y manejo de los RAEE. Así mismo, fueron definidos dos escenarios de evaluación, el primero es el estado inicial o natural que corresponde al sistema sin ninguna estrategia y el segundo es el sistema con la implementación de las estrategias, las cuales se dividieron en dos grupos. Uno es Estrategias de economía circular, educación ambiental y fomento de empleo, y el otro grupo contiene las estrategias de responsabilidad extendida del productor, estímulos de la ciudadanía y tarifa de recolección. Las simulaciones del modelo y comparaciones los escenarios, mostraron que el primer grupo de estrategias disminuyeron la tasa de generación de RAEE. De igual manera, permitieron evaluar segundo grupo de estrategias sobre la tasa de disposición. De igual manera El modelo propuesto para la gestión de Residuos de Aparatos Eléctricos y Electrónicos es útil, para la evaluación de estrategias de gestión de residuos en distintos escenarios. Abstract This paper presents a model for the evaluation of strategies in the management of Waste Electrical and Electronic Equipment (WEEE). Waste represents a risk to public health and the environment, the dangerous type compounds that constitute them and the increase of their generation. In Colombia, there is a law of 1672 guidelines for the adoption of a policy that improves the management of WEEE. This Law proposes public management objectives, of which in this article three of them were evaluated (Reduction in generation, incentive to use, promote integrated participation). For this evaluation, a model was built using the Dynamics of Systems methodology, which allowed the establishment of the socio-environmental system structure for the generation and management of WEEE. Likewise, the evaluation scenarios were defined, the first is the initial or natural state that corresponds to the system without any strategy and the second is the system with the implementation of the strategies, which were divided into two groups. One is Economic Circular Strategies, Environmental Education and Job Promotion, and the other group contains the producer's extended liability strategies, citizenship incentives and the collection rate. Model simulations and scenario comparisons showed that the first group of strategies decreased in the generation rate of WEEE. Likewise, they allowed a second group of strategies on disposition rate. Likewise, the proposed model for the management of Waste Electrical and Electronic Equipment is useful for the evaluation of waste management strategies in different scenarios.

En el sector El Ocho Letras la ganadería es un significativo causante de la degradación de la vegetación, hume- dales naturales, y el recurso hídrico. Esto conlleva a la necesidad de conocer y comprender la evolución de la cantidad de ejemplares de las diferentes edades del ganado, a lo largo del tiempo, y el efecto de las distintas variables exógenas sobre el comportamiento del sistema. A este propósito, en el presente estudio se aplica la Dinámica de Sistemas para la representación del comportamiento del número de ejemplares de ganadería del predio Laguna Negra, localizado en el sector El Ocho Letras. Se definieron como variables el número de ejemplares de ganado en las distintas edades del ciclo de vida. Los ejemplares pasan por las distintas edades, en cada una de ellas demoran un año. Para la definición de los flujos entre una y otra edad se consideraron flujos retardados. Se considera una estrategia de control para limitar el número de ejemplares mayores de un año. Se planteó un modelo matemático en tiempo discreto y se realizó simulación, obteniéndose un comportamiento oscilatorio periódico para las variables. Algunas de las principales contribuciones del trabajo están relacionadas con: análisis del efecto de variables exógenas sobre el comportamiento de las variables de nivel; planteamiento del control del número de ejemplares mayores de un año de edad basado en venta de crías hembra; desarrollo del modelo matemático a tiempo discreto, utilizando el método de cadena con flujos retardados. En el sector El Ocho Letras la ganadería es un significativo causante de la degradación de la vegetación, hume- dales naturales, y el recurso hídrico. Esto conlleva a la necesidad de conocer y comprender la evolución de la cantidad de ejemplares de las diferentes edades del ganado, a lo largo del tiempo, y el efecto de las distintas variables exógenas sobre el comportamiento del sistema. A este propósito, en el presente estudio se aplica la Dinámica de Sistemas para la representación del comportamiento del número de ejemplares de ganadería del predio Laguna Negra, localizado en el sector El Ocho Letras. Se definieron como variables el número de ejemplares de ganado en las distintas edades del ciclo de vida. Los ejemplares pasan por las distintas edades, en cada una de ellas demoran un año. Para la definición de los flujos entre una y otra edad se consideraron flujos retardados. Se considera una estrategia de control para limitar el número de ejemplares mayores de un año. Se planteó un modelo matemático en tiempo discreto y se realizó simulación, obteniéndose un comportamiento oscilatorio periódico para las variables. Algunas de las principales contribuciones del trabajo están relacionadas con: análisis del efecto de variables exógenas sobre el comportamiento de las variables de nivel; planteamiento del control del número de ejemplares mayores de un año de edad basado en venta de crías hembra; desarrollo del modelo matemático a tiempo discreto, utilizando el método de cadena con flujos retardados.

Este trabajo presenta parte de la experiencia acumulada en lautilización de la Dinámica de Sistemas, como herramienta para laeducación ambiental de estudiantes de ingeniería de laUniversidad Sergio Arboleda. A partir de la Dinámica deSistemas, se recrean diversos escenarios que permiten alestudiante tener una percepción sistémica del mundo real yvisualizar su dinámica. Dado que el medio ambiente es unsistema complejo, la utilización de la Dinámica de Sistemasfavorece la identificación de relaciones no lineales entre losatributos ambientales, la modelización y la extensión a otrastécnicas de comprensión como lo es la teoría matemática de lossistemas dinámicos, favoreciendo así la inclusión de lo ambientalde forma transversal en el currículo, pero además, permitiendo laapropiación de elementos indispensables en el ejercicioprofesional de un ingeniero. De este modo, presentamos tresejemplos de trabajos con Dinámica de Sistemas que se puedenimplementar con estudiantes de ingeniería para introducirconceptos ambientales, que fueron desarrollados en la línea deinvestigación de Ciencias de la Complejidad y Medio Ambientede la Universidad Sergio Arboleda, con algunos de susestudiantes de ingeniería. Se concluye que la utilización de laDinámica de Sistemas en la enseñanza de conceptosambientales, actúa como pauta que conecta diferentes camposdel conocimiento requeridos para la comprensión de la situaciónambiental actual del planeta, convirtiéndose así en unaherramienta para la transdisciplinariedad en ingenierías. This paper presents part of the experience gained in usingsystem dynamics as a tool for environmental education ofengineering students from Universidad Sergio Arboleda. From,diverse scenarios that allow students to have a systemic view ofthe real world and visualize its dynamics, System Dynamics arerecreated. Since the environment is a complex system, using System Dynamics favors the identification of nonlinear relationships between the environmental attributes, modeling and extension to other techniques such as understanding the mathematical theory of systems dynamic, thus contributing to the inclusion of environmental issues in a cross-curricular manner, but also allowing the appropriation of the necessary elements in the professional exercise as an engineer. This way, three examples of work with system dynamics are presented which can be implemented with engineering students to introduce environmental concepts that were developed by the research line of Sciences of Complexity and Environment of Universidad Sergio Arboleda, with some of their engineering students. It is concluded that the use of System Dynamics in the teaching of environmental concepts acts as a guideline that connects different fields of knowledge required for understanding the planet's current environmental situation, thus becoming a transdisciplinary tool in engineering.

Non-smooth systems (namely piecewise-smooth systems) have received much attention in the last decade. Many contributions in this area show that theory and applications (to electronic circuits, mechanical systems, …) are relevant to problems in science and engineering. Specially, new bifurcations have been reported in the literature, and this was the topic of this minisymposium. Thus both bifurcation theory and its applications were included. Several contributions from different fields show that non-smooth bifurcations are a hot topic in research. Thus in this paper the reader can find contributions from electronics, energy markets and population dynamics. Also, a carefully-written specific algebraic software tool is presented.

This research was developed from the interests of authors by giving their students the opportunity to have a mindset that allows them to succeed in the different processes of solving problems they will face in college, their families and community. The book is structured in three parts: introduction to complex thinking, the General Systems Theory and system dynamics, so that authors and perspectives aimed at this objective are covered.

Este documento es el producto del trabajo de un grupo interdisciplinario de investigación de la Universidad EAN, cuyo propósito es el de contribuir con la formación de los estudiantes que están iniciando su carrera profesional. El objetivo principal de este texto es desarrollar en los estudiantes el pensamiento complejo a través del estudio de casos, la utilización de diagramas casuales y la construcción de un proyecto personal que les permita ser estrategas competentes a nivel empresarial, académico y humano dentro de sus respectivas áreas de estudio. This document is product of the work of the EAN University interdisciplinary research group in its desire to contribute to the education of students who are starting their careers. Its purpose is to develop complex thinking through the study of cases, the use of casual diagrams and the construction of a personal project, allowing them to be competent strategists at business, academic, and human levels.