A Unified Approach to Piecewise Linear Hopf and Hopf-Pitchfork Bifurcations

2015 ◽  
pp. 173-184
Author(s):  
Enrique Ponce ◽  
Javier Ros ◽  
Elísabet Vela
Keyword(s):  
Piecewise Linear ◽  
Unified Approach ◽  
Pitchfork Bifurcations

Effect of Structural Nonlinearity on a Piecewise Linear Aeroelastic System

2019 ◽  
Author(s):  
János Lelkes ◽  
Tamás Kalmár-Nagy
Keyword(s):  
Piecewise Linear ◽  
Flexible Structures ◽  
Piecewise Linear Function ◽  
Aeroelastic System ◽  
Structural Nonlinearity ◽  
Structural Nonlinearities ◽  
Effective Angle ◽  
Pitchfork Bifurcations ◽  
Stability And Bifurcations ◽  
Inertia Forces

Abstract Aeroelasticity is the study of the interaction of aerodynamic, elastic and inertia forces. When flexible structures, such as an airfoil, undergo wind excitation, divergence or flutter instability may arise. We study the dynamics of a two-degree-of-freedom (pitch and plunge) aeroelastic system with cubic structural nonlinearities. The aerodynamic forces are modeled as a piecewise linear function of the effective angle of attack. Stability and bifurcations of equilibria are analyzed. The effect of the structural nonlinearity is investigated. We find border collision, rapid, Hopf, saddle-node and pitchfork bifurcations. Bifurcation diagrams of the system were calculated utilizing MatCont and Mathematica.

A Unified Approach to Study the Thermal Dynamics in Multilongitudinal Mode Semiconductor Lasers

2001 ◽  
Vol 20 (2) ◽  
pp. 159-169 ◽  
Author(s):  
M. Ganesh Madhan ◽  
P. R. Vaya ◽  
N. Gunasekaran
Keyword(s):  
Semiconductor Lasers ◽  
Unified Approach ◽  
Thermal Dynamics

Chaos in a manifold piecewise linear system

1981 ◽  
Vol 64 (10) ◽  
pp. 9-17 ◽  
Author(s):  
Toshimichi Saito ◽  
Hiroichi Fujita
Keyword(s):  
Linear System ◽  
Piecewise Linear ◽  
Piecewise Linear System
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