scholarly journals Stable periodic solutions in the forced pendulum equation

2013 ◽  
Vol 18 (6) ◽  
pp. 585-599 ◽  
Author(s):  
Rafael Ortega
Keyword(s):  
Periodic Solutions ◽  
Pendulum Equation ◽  
Stable Periodic ◽  
Forced Pendulum

Periodic Solutions of Pendulum-Like Hamiltonian Systems in the Plane

2012 ◽  
Vol 12 (2) ◽  
Author(s):  
Alessandro Fonda ◽  
Rodica Toader
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Hamiltonian Systems ◽  
Point Theorem ◽  
Elementary Level ◽  
Pendulum Equation ◽  
Forced Pendulum ◽  
The One

AbstractBy the use of a generalized version of the Poincaré-Birkhoff fixed point theorem, we prove the existence of at least two periodic solutions for a class of Hamiltonian systems in the plane, having in mind the forced pendulum equation as a particular case. Our approach is closely related to the one used by Franks in [15], but the proof remains at a more elementary level.

scholarly journals Prevalence of stable periodic solutions in the forced relativistic pendulum equation

2018 ◽  
Vol 23 (10) ◽  
pp. 4579-4594
Author(s):  
Feng Wang ◽  
◽  
Jifeng Chu ◽  
Zaitao Liang ◽  
◽  
...  
Keyword(s):  
Periodic Solutions ◽  
Pendulum Equation ◽  
Stable Periodic

Periodic solutions of the forced pendulum equation with friction

2003 ◽  
Vol 14 (7) ◽  
pp. 311-320
Author(s):  
Pablo Amster ◽  
Maria Cristina Mariani
Keyword(s):  
Periodic Solutions ◽  
Pendulum Equation ◽  
Forced Pendulum

Prevalence of Non-degenerate Periodic Solutions in the Forced Pendulum Equation

2013 ◽  
Vol 13 (1) ◽  
Author(s):  
Rafael Ortega
Keyword(s):  
Periodic Solutions ◽  
Main Tool ◽  
Main Question ◽  
Residual Set ◽  
Pendulum Equation ◽  
Transversality Theorem ◽  
Classical Duality ◽  
Forced Pendulum

AbstractMany known properties of the forced pendulum equation are generic. This means that they hold on a residual set of forcings. The classical duality category/measure inspires the main question in the paper: are these properties also valid for a prevalent set of forcings? This is the case for a key property: the non-degeneracy of periodic solutions. The main tool in the proof is a prevalent version of the parametric transversality theorem.

Hopf Bifurcation Induced by Delay Effect in a Diffusive Tumor-Immune System

2018 ◽  
Vol 28 (11) ◽  
pp. 1850136 ◽  
Author(s):  
Ben Niu ◽  
Yuxiao Guo ◽  
Yanfei Du
Keyword(s):  
Immune System ◽  
Hopf Bifurcation ◽  
Periodic Solutions ◽  
Center Manifold ◽  
Immune Cell ◽  
Tumor Treatment ◽  
Delay Effect ◽  
Stable Periodic ◽  
The Stability ◽  
Bifurcation And Stability

Tumor-immune interaction plays an important role in the tumor treatment. We analyze the stability of steady states in a diffusive tumor-immune model with response and proliferation delay [Formula: see text] of immune system where the immune cell has a probability [Formula: see text] in killing tumor cells. We find increasing time delay [Formula: see text] destabilizes the positive steady state and induces Hopf bifurcations. The criticality of Hopf bifurcation is investigated by deriving normal forms on the center manifold, then the direction of bifurcation and stability of bifurcating periodic solutions are determined. Using a group of parameters to simulate the system, stable periodic solutions are found near the Hopf bifurcation. The effect of killing probability [Formula: see text] on Hopf bifurcation values is also discussed.

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