Results 291 to 300 of about 766,070 (327)

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.
H. S. Hassan, K. Y. Guan, J. Gunson
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Periodic solutions of the pendulum

Journal of Physics A: Mathematical and General, 2000
Summary: We 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, M Y Kucinski   +1 more
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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
openaire   +4 more sources

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
openaire   +3 more sources

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 ...
openaire   +2 more sources