Chaotic Vibration of a Two-dimensional Non-strictly Hyperbolic Equation Academic Article

abstract

• AbstractThe study of chaotic vibration for multidimensional PDEs due to nonlinear boundary conditions is challenging. In this paper, we mainly investigate the chaotic oscillation of a two-dimensional non-strictly hyperbolic equation due to an energy-injecting boundary condition and a distributed self-regulating boundary condition. By using the method of characteristics, we give a rigorous proof of the onset of the chaotic vibration phenomenon of the zD non-strictly hyperbolic equation. We have also found a regime of the parameters when the chaotic vibration phenomenon occurs. Numerical simulations are also provided.

authors

• Chen, Goong

published proceedings

• CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES

author list (cited authors)

• Li, L., Tian, J., & Chen, G.

citation count

• 8

complete list of authors

• Li, Liangliang||Tian, Jing||Chen, Goong

publication date

• December 2018

publisher

• Canadian Mathematical Society  Publisher

published in

• Canadian Mathematical Bulletin  Journal

keywords

• Chaotic Vibration
• Method Of Characteristics
• Period-doubling Bifurcation
• Reflection Boundary Condition

Digital Object Identifier (DOI)

• 10.4153/CMB-2018-012-1

start page

• 768

end page

• 786

volume

• 61

issue

• 4

URL

• http://dx.doi.org/10.4153/cmb-2018-012-1