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Periodic solutions of periodic Riccati equations
IEEE Transactions on Automatic Control, 1984For 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 +2 more
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The existence of periodic solutions
1999Abstract Suppose that the phase diagram for a differential equation contains a single, unstable equilibrium point and a limit cycle surrounding it, as in the case of the van der Pol equation. Then in practice all initial states lead to the periodic oscillation represented by the limit cycle.
D W Jordan, P Smith
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Periodic Solutions of Periodic Systems [PDF]
, 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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Bifurcation of Forced T-Periodic Solutions into Asymptotically Quasi-Periodic Solutions
1980In Chapter IX we determined the conditions under which subharmonic solutions, nT-periodic solutions with integers n ≥1, could bifurcate from forced T-periodic solutions. That is to say, we looked for the conditions under which nonautonomous, T-periodic differential equations give rise to subharmonic solutions when the Floquet exponents at criticality ...
Daniel D. Joseph, Gérard Iooss
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Periodic solutions of periodic differential equations
Journal of the Nigerian Association of Mathematical Physics, 2008In this paper we extend the work of Bello [4] where he considered the periodic solutions of certain dynamical systems inside a cylindrical phase space with differential equations of the form yn-1⓫yn-1+...+αn-1y(1) + f(y1..,yn-1,y) = 0 (\'=ddt (+) with the property that there is a ω>0 and a natural number K such that y (t+w) = y(t) + k ...
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Convergence to periodic solutions
Journal of Difference Equations and Applications, 2001Open Problems and Conjectures Edited by Gerry Ladas In this section we present some open problems and conjectures about some interesting types of difference equations.
A.M. Amleh, G. Ladas
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Periodic solutions of the pendulum
Journal of Physics A: Mathematical and General, 2000We develop an analytical procedure to determine orbits that a harmonically driven, damped pendulum describes in the phase plane. The theory predicts the existence of more than one solution for the same system, depending on initial conditions. Also, it predicts a stable solution around the top position of the pendulum.
Luiz Henrique Alves Monteiro +1 more
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Periodic solutions and locking-in on the periodic surface
International Journal of Non-Linear Mechanics, 1973Abstract Periodic solutions (on the torus) are studied for the differential equation on the torus θ ' = 1 + ge ‖( t / T ), θ , T , ϵ ). This equation, for example, governs solutions on the periodic surface for a periodically perturbed autonomous system. The set of all points in a horizontal strip of the T — ϵ plane containing ϵ = 0 for which
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The Bifurcation of T-periodic Solutions into nT-periodic Solutions and TORI
1977My lecture on bifurcation and stability of solutions which branch from forced T-periodic solutions is based on the recent work of G. IOOSS and myself [1] and on my forthcoming paper on factorization theorems [2]. In general, forced T-periodic solutions bifurcate into subharmonic solutions with a fixed period τ(τ=nT; n=1,2,3,4) independent of the ...
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Existence Theorems for Periodic Solutions and Almost Periodic Solutions
1975First of all, we shall state some fixed point theorems without proofs. The following theorem is due to Brouwer. For the proof, see [5].
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