Results 281 to 290 of about 171,261 (295)

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 the existence of periodic solutions and almost periodic solutions for nonlinear systems

Nonlinear Analysis: Theory, Methods & Applications, 1995
The author presents dissipative type conditions which guarantee the existence and uniqueness of bounded, periodic and almost periodic solutions of a system \(x'= A(t, x)+ f(t)\), where the right-hand side is corresponding periodic or almost periodic.
Masato Imai, Shigeo Kato
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The existence of periodic solutions

1999
Abstract 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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Existence of periodic solutions

Mathematical Notes, 1997
The author develops an apparatus for proving the existence of periodic solutions to differential equations \(y'(t)=Ay(t)+f(t,y(t))\) and to differential inclusions \(y'(t)\in Ay(t)+F(t,y(t))\). Here, \(A\) is a constant \(n\times n\) matrix, \(f\) is a Carathéodory function, and \(F\) is a Carathéodory multifunction. If the equation \(y'(t)=Ay(t)\) has
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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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Periodic solutions and locking-in on the periodic surface

International Journal of Non-Linear Mechanics, 1973
Abstract 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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Bifurcation of Forced T-Periodic Solutions into Asymptotically Quasi-Periodic Solutions

1980
In 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, 2008
In 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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The Bifurcation of T-periodic Solutions into nT-periodic Solutions and TORI

1977
My 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

1975
First 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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