Dynamics of a System Associated with a Piecewise Quadratic Family / Dinámica de un sistema asociado a una familia cuadrática a tramos

Dynamics of a System Associated with a Piecewise Quadratic Family / Dinámica de un sistema asociado a una familia cuadrática a tramos

AbstractThis paper presents a study, both in analytical and numerical form, of a discrete dynamical system associated with a piecewise quadratic family. The orbits of periods one and two are characterized, and their stability is established. The nonsmooth phenomenon known as border collision is pres...

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Bibliographic Details
Main Authors: LOPEZ BURITICA, KAREN, Casanova Trujillo, Simeón, Acosta Medina, Carlos Daniel
Format: Online
Language:spa
Published: Universidad Pedagógica y Tecnológica de Colombia 2016
Subjects:
Bifurcaciones
caos
estabilidad
órbita periódica
punto fijo
sistema dinámico.
Sistemas Dinámicos
Online Access:https://revistas.uptc.edu.co/index.php/ciencia_en_desarrollo/article/view/3951
Description
Summary:AbstractThis paper presents a study, both in analytical and numerical form, of a discrete dynamical system associated with a piecewise quadratic family. The orbits of periods one and two are characterized, and their stability is established. The nonsmooth phenomenon known as border collision is present when there is a period doubling. Lyapunov exponents are calculated numerically to determine the presence of chaos in the system. ResumenPresenta un estudio analítico y numérico de la dinámica de un sistema discreto asociado a una familiacuadrática a tramos; se caracterizan las órbitas de período uno y dos, así como su estabilidad; se muestrala presencia del fenómeno no suave, conocido como bifurcación por colisión de borde cuando ocurre undoblamiento de período. Se hallaron numéricamente los exponentes de Lyapunov para detectar la presencia de caos en el sistema.