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Periodic solutions of pendulum: II
Journal of Physics A: Mathematical and General, 2003Summary: 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
1994In 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 of Integrodifferential Equations
Journal of the London Mathematical Society, 1985The author is investigating the existence of periodic solutions to the integrodifferential equation of Volterra type \[ (1)\quad x'(t)=h(t,x(t))+\int^{t}_{-\infty}q(t,s,x(s))ds, \] under the basic assumptions that \(h: R\times R^ n\to R^ n\), and \(q: R\times R\times R^ n\to R^ n\) are both continuous, h is periodic in t with period T, and \(q(t+T,s+T ...
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Periodic and Unbounded Solutions of Periodic Systems
Bulletin of the Malaysian Mathematical Sciences SocietyzbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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 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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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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2011
This chapter presents existence and stability of almost periodic solutions of the following system \( {\frac{dx(t)}{dt}} = A(t)x(t) + f(t,x(\theta_{\upsilon (t) - p1} ),x(\theta_{\upsilon (t) - p2} ), \ldots ,x(\theta_{\upsilon (t) - pm} )), \) (7.1) where \( x \in \mathbb{R}^{n} ,\;t \in \mathbb{R}, \) υ(t) = 1 if θ i ≤ t < θ i+1, i = …,-2,-1,0,1,2,…,
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This chapter presents existence and stability of almost periodic solutions of the following system \( {\frac{dx(t)}{dt}} = A(t)x(t) + f(t,x(\theta_{\upsilon (t) - p1} ),x(\theta_{\upsilon (t) - p2} ), \ldots ,x(\theta_{\upsilon (t) - pm} )), \) (7.1) where \( x \in \mathbb{R}^{n} ,\;t \in \mathbb{R}, \) υ(t) = 1 if θ i ≤ t < θ i+1, i = …,-2,-1,0,1,2,…,
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