Results 311 to 320 of about 7,935,743 (371)

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
openaire   +3 more sources

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
openaire   +2 more sources

Existence and Global bifurcation of periodic solutions to a Class of differential variational inequalities

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 2013
In this paper, by using the topological degree theory for multivalued maps and the method of guiding functions, the existence and global bifurcation for periodic solutions of a class of differential variational inequalities are studied.
Zhenhai Liu, N. Loi, V. Obukhovskii
semanticscholar   +1 more source

An Abstract Nash–Moser Theorem and Quasi-Periodic Solutions for NLW and NLS on Compact Lie Groups and Homogeneous Manifolds

, 2013
We prove an abstract implicit function theorem with parameters for smooth operators defined on scales of sequence spaces, modeled for the search of quasi-periodic solutions of PDEs. The tame estimates required for the inverse linearised operators at each
M. Berti, L. Corsi, M. Procesi
semanticscholar   +1 more source

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
openaire   +1 more source

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).
openaire   +1 more source

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
openaire   +3 more sources

Wronskian, Gramian, Pfaffian and periodic-wave solutions for a (3+1)-dimensional generalized nonlinear evolution equation arising in the shallow water waves

Nonlinear dynamics, 2022
Fei-Yan Liu, Yi Gao, Xin Yu, Cui-Cui Ding   +3 more
semanticscholar   +1 more source