Examinando por Materia "ECUACIONES DIFERENCIALES"
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Ítem Modelamiento, Simulación e Implementación de la Ecuación de Cardy en el Fenómeno de PercolaciónMahecha Mora, Luisa Fernanda; Vacca González, HaroldIn this paper we present the analysis, modeling, simulation and implementation of the Cardy equation in the percolation phenomenon; The design of a circuit is presented, which synthesizes this phenomenon; The implementation of the Schwarz-Christoffel transformation is deduced from the integral equation, the solution is obtained in this approximate way, solving its differential version by means of the Runge-Kutta method using a Matlab Toolbox [1] and implementing the Gaussian hypergeometric function. To observe the behavior of the circuit, the output of the system is analyzed both in the simulation and in the physical assembly; In addition, by implementing numerical methods, it approaches a solution and finally compares it with the experimental results with those obtained theoretically.Ítem Modelamiento, Simulación e Implementación del Oscilador Caótico Conmutado por TramosConde González, Nicolás Felipe; Vacca González, HaroldThis article presents the analysis, modeling, simulation, and implementation of a circuit that describes a chaotic oscillator in a switched continuous system by sections (OCCCT); Gets the system of differential equations that model it, and the approximation of the solution is implemented by the method of decomposition of Adomian (ADM). As a result, gets the corresponding mathematical development of the system that models the phenomenon. To observe the presence of chaos, the Lyapunov exponents are obtained and analyzed both output variables and the phase diagram that they generate. With the theoretical - analytical and approximate - system solution, is a comparison with data obtained from the simulation and the thrown by the implementation of the circuit.Ítem Modelamiento, Simulación e Implementación Del Oscilador Por Medio De La Ecuación De DuffingDelgado Almendrales, Jhon Sebastián; Barajas Sotelo, José de Jesús; Vacca González, HaroldThe article presents the research that led to the observation, modeling and analysis of a chaotic oscillator determined by the Duffing equation: x ̈+ εx ̇-βx+αx^3=f Cos(wt) obtained when a muffled and forced movement occurs and also the description of three solutions: the approximate analytical, physics and simulated. In this case, the system is mathematically modeled by a differential equation ordinary of second order non linear – or its respective representation as a differential equation system -. The Method of “Runge-Kutta” is applied for the solutions of the equations system, the numerical method of “Adomian decomposition” (ADM) is adopted by its implementation in MatLab R in order to provide the approximated solution to the equation, as well as the solution thrown after the implementation of the associated circuit. The chaos presence is confirmed making use of the Exponents of Lyapunov. Finally both, the output variables and the phase diagram generated were analyzed. Making the comparison between the obtained solutions by Runge-Kutta, the simulated and the one shown by the circuit design adopted.