Inverse bifurcation problem for von Karman equations
Keywords:
inverse bifurcation problem, nonlinear boundary problem for PDEs, von Karman equations
Abstract
The paper is concerned with an approach to solve inverse bifurcation problem. The approach employs solution belonged to bifurcation paths of the problem in question in order to cluster consequences of them to reveal typical consequences (bifurcation precursors, early-warning signs). The approach was applied to solve inverse bifurcation problem for von Karman equations.Downloads
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References
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Wishart D. A numerical classification methods for deriving natural classes // Nature. - 1969. - Vol. 221, - P. 97-98.
Лапко А.В., Ченцов С.В. Непараметрические системы обработки информации.– Новосибирск: Наука, 2000. – 352 с.
Kiss I.Z., Hudson J.L. Experiments on coherence resonance: Noisy precursors to Hopf bifurcations // Physical Review E. - 2003. - Vol. 67. - P. 15-19.
Kravtsov Yu.A., Surovyatkina E.D. Nonlinear saturation of prebifurcation noise amplification // Physics Letters A. - 2003. - Vol. 3199, № 3-4. - P. 348–351.
Obodan N.I., Lebedeyev O.G., Gromov V.A. Nonlinear behavior and stability of thin-walled shells. – Springer, 2013. – 180 pp.
Omberg L., Dolan K., Neiman A., Moss F. Detecting the onset of bifurcations and their precursors from noisy data // Physical Review E. - 2000. - Vol. 61, № 5. - P. 4848-4853.
Pei X., Moss F. Characterization of low-dimensional dynamics in the crayfish caudal photoreceptor // Nature. - 1996. - Vol. 379, № 6566. - P. 618-621.
Pierson D., Moss F. Detecting Periodic Unstable Points in Noisy Chaotic and Limit Cycle Attractors with Applications to Biology // Phys. Rev. Lett 75. - 1995. - Vol. 75, № 11. - P. 2124-2135.
Surovyatkina E. Prebifurcation noise amplification and noise-dependent hysteresis as indicators of bifurcations in nonlinear geophysical systems // Nonlinear Processes in Geophysics. - 2005. - Vol. 12. - P. 25-29.
Wiesenfeld K. Virtual Hopf phenomenon: A new precursor of period-doubling bifurcations d // Physical Review A. - 1985. - Vol. 32, № 3. - P. 1744- 1751.
Wishart D. A numerical classification methods for deriving natural classes // Nature. - 1969. - Vol. 221, - P. 97-98.
Published
2017-05-27
How to Cite
Адлуцкий, В. Я., Громов, В. А., & Ободан, Н. И. (2017). Inverse bifurcation problem for von Karman equations. Bulletin of V.N. Karazin Kharkiv National University, Series «Mathematical Modeling. Information Technology. Automated Control Systems», 32, 5-14. Retrieved from https://periodicals.karazin.ua/mia/article/view/8574
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