Eliminación de las Grandes Oscilaciones de un Sistema de Ecuaciones Diferenciales
Resumen
Considerando el sistema No lineal. que tiene un comportamiento oscilatorio, se demuestra en el caso que f(-x) =- f(x), que al reemplazar la función f(x) por f(x+Bsinwt), y para valores de B y w suficientemente grande el sistema no tiene movimiento oscilatorio de gran amplitud. De hecho todas las soluciones tienden a una vecindad del origen tan pequeña como se quiera.
Se prueba que para w suficientemente grande, el sistema promediado es una buena aproximación del sistema perturbado. Esto es que toda solución del sistema perturbado está suficientemente cercana a una solución del sistema promediado. Igualmente se prueba que existe Bo tal que B > Bo, la solución trivial del sistema promediado es asintóticamente estable para valores de w suficientemente grandes. Por último se prueba que para B y w suficientemente grande el sistema perturbado no tiene movimiento oscilatorio de gran amplitud, es decir, la perturbación ha aniquilado las oscilaciones de gran amplitud.
Palabras claves:
Oscilaciones, soluciones periodicas, Sistema Perturbado, Función Promedio, Eliminación de Oscilaciones, soluciones oscilatorias.
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