Estimation of chaotic thresholds for the recently proposed rotating pendulum
Abstract:
In this paper, we investigate the nonlinear behavior of the recently proposed rotating pendulum which is a cylindrically nonlinear system with irrational type having smooth and discontinuous characteristics depending on the value of a smoothness parameter. We introduce a cylindrical approximate system whose analytical solutions can be obtained successfully to reflect the nature of the original system without the barrier of irrationalities. Furthermore, Melnikov method is employed to detect the chaotic thresholds for the homoclinic orbits of the second-type, a pair of homoclinic orbits of the first and second-type and the double heteroclinic orbits under the perturbation of viscous damping and external harmonic forcing within the smooth regime. Numerical simulations show the efficiency of the proposed method and the results presented herein this paper demonstrate the pbkp_redicated chaotic attractors of pendulum-type, SD-type and their mixture depending on the coupling of the nonlinearities. © 2013 World Scientific Publishing Company.
Año de publicación:
2013
Keywords:
- singular closed orbits
- Chaotic thresholds
- Rotating pendulum
- Irrational nonlinearity
- SD oscillator
Fuente:

Tipo de documento:
Article
Estado:
Acceso restringido
Áreas de conocimiento:
- Sistema no lineal
- Sistema no lineal
- Sistema dinámico
Áreas temáticas:
- Física
- Artrópodos fósiles
- Procesos, formas y temas de la escultura