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Flexible fibers in shear flow: attracting periodic solutions

, 2019
Agnieszka M. Słowicka, Howard A. Stone, Maria L. Ekiel-Jeżewska   +2 more
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Exploring complex phenomena in fluid flow and plasma physics via the Schrödinger-type Maccari system. [PDF]

Sci Rep
Abbas N, Hussain A, Ibrahim TF, D Alanazi F, Oğul B, Aly ES, Herrera J.   +6 more
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Periodic Solutions; Averaging Methods

1999
Abstract Consider an equation of the form x εh(x, x) x 0 where ε is small. Such an equation is in a sense close to the simple harmonic equation x x 0, whose phase diagram consists of circles centred on the origin. It should be possible to take advantage of this fact to construct approximate solutions: the phase paths will be nearly ...
D W Jordan, P Smith
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Periodic solutions of periodic Riccati equations

IEEE Transactions on Automatic Control, 1984
Summary: For periodically time-varying matrix Riccati equations, controllability and observability (in the usual sense) are shown to be sufficient for the existence of a unique positive definite periodic solution.
BITTANTI, SERGIO, COLANERI, PATRIZIO, GUARDABASSI, GUIDO   +2 more
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On Periodic Solutions of the Periodic

Results in Mathematics, 1988
By treating the periodic Riccati equation $${\rm\dot{z}=a(t)z^2+b(t)z+c(t)}$$ as a dynamical system on the sphere S, the number and stability of its periodic solutions are determined. Using properties of Moebius transformations, an exact algebraic relation is obtained between any periodic solution and any complex-valued periodic solution.
K. Y. Guan, J. Gunson, H. S. Hassan
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Almost Periodic Solutions for Limit Periodic Systems

SIAM Journal on Applied Mathematics, 1972
A system of ordinary differential equations with limit periodic t-dependence has associated with it a sequence of approximating systems with periodic t-dependence. If each of these approximating systems has a periodic solution, sufficient conditions are given on these solutions under which the original system has an almost periodic solution. Additional
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Breather Solutions in Periodic Media

Communications in Mathematical Physics, 2011
The authors consider nonlinear wave equations of the form \[ s(x) u_{tt} = u_{xx} - q(x) u + u^3, \] where \(s(x)\) and \(q(x)\) are \(a\)-periodic real-valued coefficients. They choose these coefficients in such a way that the linear problem, \[ q(x) w(x) - w''(x) - \omega^2 s(x) w(x) = 0, \] has finite spectral gaps near odd multiples of \(\omega_* =
Blank, Carsten, Chirilus-Bruckner, Martina, Lescarret, Vincent, Schneider, Guido   +3 more
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Periodic solutions of pendulum: II

Journal of Physics A: Mathematical and General, 2003
Summary: Period-3 oscillations of pendulum are investigated using the method developed in our previous paper [ibid. 33, No. 47, 8489--8505 (2000; Zbl 0972.70020)]. Values of the driving force within very narrow ranges may give rise to this kind of motion.
Kucinski, M. Y., Monteiro, L. H. A.
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Periodic planar systems without periodic solutions

Qualitative Theory of Dynamical Systems, 2001
\textit{D. Miklaszewski} [Bull. Belg. Math. Soc. 3, No. 2, 239-242 (1996; Zbl 0848.34028)] found that the differential equation \[ \frac{dz}{dt}=z^2+r e^{i t} \] has no periodic solutions for some choice of the parameter \(r\) provided that the following conjecture is true. There is some integer \(N\) such that the elements of the sequence defined by \(
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Periodic Solutions of Periodic Systems

1994
In this chapter we study the existence, stability and isolation of periodic solutions belonging to n-dimensional systems of periodic nonlinear differential equations of the form ẋ = f (t, x) where f is periodic in t with some period T > 0: f (t + T, x) = f (t,x).
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