Buradasınız

Analyzing Periodic Solutions of an ODE Suspension Bridge Model using Difference Equations and Polynomial Methods

Journal Name:

Publication Year:

Author Name
Abstract (2. Language): 
In [13], McKenna and Moore studied oscillations in a suspension bridge by investigating periodic solutions to a differential equations model for the bridge and its linearized version numerically. In this paper, the author seeks to build a rigorous mathematical foundation for the numerical experi¬ments of McKenna and Moore in [13] by studying an associated discrete difference equations model using an interplay of ideas from engineering, discrete dynamical systems, algebraic geometry and the theory of polynomials.
442
461

REFERENCES

References: 

[1] S. Altin, K. Kaptan and S. S. Tezcan. Dynamic Analysis of Suspension Bridges and Full Scale Testing, Open Journal of Civil Engineering 2, 58-67, 2012.
[2] S. Basu and O. Merino. On the Global Behavior of Solutions to a Planar System of Difference Equations, Communications on Applied Nonlinear Analysis 16(1), 89-101, 2009.
[ 3] S. Basu. The Role of Plane Algebraic Curves in the Global Dynamics of a Class of Planar Nonlinear Discrete Dynamical Systems, Advances in Difference Equations 2013:292, 2013.
[ 4] S. Basu. Global Behavior of Solutions to a Class of Second-Order Rational Difference Equations when Prime Period-Two Solutions Exist, Journal ofDifference Equations and Applications 18,Issue 5, 1-29, 2012.
[5] E. Dancer and P Hess. Stability of fixed points for order preserving discrete-time dynamical systems, Journal für die reine und angewandte Mathematik 419, 125-139, 1991.
[6] M. S. T. De Freitas, R. L. Viana and C. Grebogi. Basins of Attraction of Periodic Oscillations in Suspension Bridges, Nonlinear Dynamics 37, 207-226,2004.
[ 7] M. S. T. De Freitas, R. L. Viana and C. Grebogi. Multistability, Basin Boundary Structure, and Chaotic Behavior in a Suspension Bridge Model, International Journal ofBifurcation and Chaos 14(3), 927-950, 2004.
[ 8] Z. Ding. On Nonlinear Oscillations in a Suspension Bridge System, Transactions ofthe American Mathematical Society 354(1), 265-274, 2001.
[9] S. Elaydi. An Introduction to Difference Equations, 2nd ed., Springer-Verlag, New York,
1999.
[10] S. Elaydi. Discrete Chaos with Applications in Science and Engineering, 2nd ed., Chapman-
Hall, Boca Raton, FL, 2008.
[11] M. Hirsch and H. Smith. Monotone Dynamical Systems, Handbook ofDifferential Equa¬tions: OrdinaryDifferential Equations. Vol. II, 239-357, Elsevier B. V., Amsterdam, 2005.
[12] M. R. S. Kulenovic and O. Merino. Competitive-Exclusion versus Competitive-Coexistence for Systems in the Plane, Discrete and Continuous Dynamical Systems Series B 6, 1141¬1156, 2006.
[13] P. J. McKenna and K. S. Moore. Multiple periodic solutions to a suspension bridge ordi¬nary differential equation, Proceedings ofthe Conference on Nonlinear Differential Equa¬tions (Coral Gables, FL, 1999). Vol. 5, 2000.
[14] A. Pascoletti and F. Zanolin. Example of a suspension bridge ODE model exhibiting chaotic dynamics: A topological approach, Journal ofMathematical Analysis and Appli¬cations 339, 1179-1198, 2008.
REFERENCES
461
[15] H. Smith. Planar Competitive and Cooperative Difference Equations, Journal of Difference Equations and Applications 3, 335-357, 1998.
[16] R. J. Walker. Algebraic Curves, Princeton University Press, 1950.

Thank you for copying data from http://www.arastirmax.com