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Canessa, E., & Riolo, R. L. (2006). An agent-based model of the impact of computer-mediated communication on organizational culture and performance: an example of the application of complex systems analysis tools to the study of CIS. J. Inf. Technol., 21(4), 272–283.
Abstract: Organizations that make use of computer information systems (CIS) are prototypical complex adaptive systems (CAS). This paper shows how an approach from Complexity Science, exploratory agent-based modeling (ABM), can be used to study the impact of two different modes of use of computer-mediated communication (CMC) on organizational culture (OC) and performance. The ABM includes stylized representations of (a) agents communicating with other agents to complete tasks; (b) an OC consisting of the distribution of agent traits, changing as agents communicate; (c) the effect of OC on communication effectiveness (CE), and (d) the effect of CE on task completion times, that is, performance. If CMC is used in a broad mode, that is, to contact and collaborate with many, new agents, the development of a strong OC is slowed, leading to decreased CE and poorer performance early on. If CMC is used in a local mode, repeatedly contacting the same agents, a strong OC develops rapidly, leading to increased CE and high performance early on. However, if CMC is used in a broad mode over longer time periods, a strong OC can develop over a wider set of agents, leading to an OC that is stronger than an OC which develops with local CMC use. Thus broad use of CMC results in overall CE and performance that is higher than is generated by local use of CMC. We also discuss how the dynamics generated by an ABM can lead to a deeper understanding of the behavior of a CAS, for example, allowing us to better design empirical longitudinal studies.
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Dumett, M. A., & Cominetti, R. (2018). On The Stability Of An Adaptive Learning Dynamics In Traffic Games. J. Dyn. Games, 5(4), 265–282.
Abstract: This paper investigates the dynamic stability of an adaptive learning procedure in a traffic game. Using the Routh-Hurwitz criterion we study the stability of the rest points of the corresponding mean field dynamics. In the special case with two routes and two players we provide a full description of the number and nature of these rest points as well as the global asymptotic behavior of the dynamics. Depending on the parameters of the model, we find that there are either one, two or three equilibria and we show that in all cases the mean field trajectories converge towards a rest point for almost all initial conditions.
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Goles, E., Lobos, F., Montealegre, P., Ruivo, E. L. P., & de Oliveira, P. P. B. (2020). Computational Complexity of the Stability Problem for Elementary Cellular Automata. J. Cell. Autom., 15(4), 261–304.
Abstract: Given an elementary cellular automaton and a cell v, we define the stability decision problem as the determination of whether or not the state of cell v will ever change, at least once, during the time evolution of the rule, over a finite input configuration. Here, we perform the study of the entire elementary cellular automata rule space, for the two possible decision cases of the problem, namely, changes in v from state 0 to 1 (0 -> 1), and the other way round (1 -> 0). Out of the 256 elementary cellular automata, we show that for all of them, at least one of the two decision problems is in the NC complexity class.
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Gonzalez, E., & Villena, M. J. (2011). Spatial attrition modeling: Stability conditions for a 2D + t FD formulation. Comput. Math. Appl., 61(11), 3246–3257.
Abstract: A new general formulation for the spatial modeling of combat is presented, where the main drivers are movement attitudes and struggle evolution. This model in its simplest form is represented by a linear set of two coupled partial differential equations for two independent functions of the space and time variables. Even though the problem has a linear shape, non-negative values for the two functions render this problem as nonlinear. In contrast with other attempts, this model ensures stability and theoretical consistency with the original Lanchester Equations, allowing for a better understanding and interpretation of the spatial modeling. As a numerical illustration a simple combat situation is developed. The model is calibrated to simulate different troop movement tactics that allow an invader force to provoke maximum damage at a minimum cost. The analysis provided here reviews the trade-off between spatial grid and time stepping for attrition cases and then extends it to a new method for guaranteeing good numerical behavior when the solution is expected to grow along the time variable. There is a wide variety of spatial problems that could benefit from this analysis. (C) 2011 Elsevier Ltd. All rights reserved.
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Gonzalez-Olivares, E., Gonzalez-Yanez, B., Becerra-Klix, R., & Ramos-Jiliberto, R. (2017). Multiple stable states in a model based on predator-induced defenses. Ecol. Complex., 32, 111–120.
Abstract: A large variety of antipredator defenses are exhibited by plants, animals and microbes in nature. A deep understanding of the dynamic consequences of prey responses to predation risk is essential for building a comprehensive theory of food webs. Here we present a simple classification of prey defenses based on the sensitivity of prey immunity to predation respect to abundances of prey and predators. Only three out of six defense types have been analytically studied in the context of predator-prey dynamics, which reveals a serious gap in our current knowledge of ecological interactions. In this study we present a mathematical analysis on a widely occurring type of prey defense whose behavior has not been established in exact terms. The study model considers prey whose average immunity to predators is enhanced by predator abundance. This case, known as inducible defenses, has been reported for a wide array of species. Our results reveal a rich dynamic behavior, in which the predator-prey system exhibits either one, two or three positive equilibrium points, with up to two attractors. Thus, inducible defenses constitute a mechanism that could drive alternative stable states even in very simple food web models. (C) 2017 Elsevier B.V. All rights reserved.
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Moffat, R., Caceres, C., & Tapia, E. (2021). Rock Pillar Design Using a Masonry Equivalent Numerical Model. Energies, 14(4), 890.
Abstract: In underground mining, the design of rock pillars is of crucial importance as these are structures that allow safe mining by maintaining the stability of the surrounding excavations. Pillar design is often a complex task, as it involves estimating the loads at depths and the strength of the rock mass fabric, which depend on the intact strength of the rock and the shape of the pillar in terms of the aspect ratio (width/height). The design also depends on the number, persistence, orientation, and strength of the discontinuities with respect to the orientation and magnitude of the stresses present. Solutions to this engineering problem are based on one or more of the following approaches: empirical design methods, practical experience, and/or numerical modeling. Based on the similarities between masonry structures and rock mass characteristics, an equivalent approach is proposed as the one commonly used in masonry but applied to rock pillar design. Numerical models using different geometric configurations and state of stresses are carried out using a finite difference numerical approach with an adapted masonry model applied to rocks. The results show the capability of the numerical approach to replicate common types of pillar failure modes and stability thresholds as those observed in practice.
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Vera-Damian, Y., Vidal, C., & Gonzalez-Olivares, E. (2019). Dynamics and bifurcations of a modified Leslie-Gower-type model considering a Beddington-DeAngelis functional response. Math. Meth. Appl. Sci., 42(9), 3179–3210.
Abstract: In this paper, a planar system of ordinary differential equations is considered, which is a modified Leslie-Gower model, considering a Beddington-DeAngelis functional response. It generates a complex dynamics of the predator-prey interactions according to the associated parameters. From the system obtained, we characterize all the equilibria and its local behavior, and the existence of a trapping set is proved. We describe different types of bifurcations (such as Hopf, Bogdanov-Takens, and homoclinic bifurcation), and the existence of limit cycles is shown. Analytic proofs are provided for all results. Ecological implications and a set of numerical simulations supporting the mathematical results are also presented.
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Villena, M. J., & Araneda, A. A. (2017). Dynamics and stability in retail competition. Math. Comput. Simul., 134, 37–53.
Abstract: Retail competition today can be described by three main features: (i) oligopolistic competition, (ii) multi-store settings, and (iii) the presence of large economies of scale. In these markets, firms usually apply a centralized decisions making process in order to take full advantage of economies of scales, e.g. retail distribution centers. In this paper, we model and analyze the stability and chaos of retail competition considering all these issues. In particular, a dynamic multi-market Cournot Nash equilibrium with global economies and diseconomies of scale model is developed. We confirm the non-intuitive hypothesis that retail multi-store competition is more unstable than traditional small business that cover the same demand. The main sources of stability are the scale parameter, the number of markets, and the number of firms. (C) 2016 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.
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