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Desynchronization by periodic orbits
Physical Review E, 1995Synchronous chaotic behavior is often interrupted by bursts of desynchronized behavior. We investigate the role of unstable periodic orbits in bursting events and show that they serve as sources of local transverse instability within a synchronous chaotic attractor. Analysis of bursts in both model and experimental studies of two coupled R\"ossler-like
, Heagy, , Carroll, , Pecora
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Targeting unstable periodic orbits
Physical Review E, 1995Specific targeting of unstable periodic orbits has been achieved by using large-amplitude perturbations in a dynamical system. The method has been demonstrated experimentally on a ${\mathrm{CO}}_{2}$ laser with modulated losses whose unstable periodic orbits are created either at a period-doubling or at a saddle-node bifurcation.
, Chizhevsky, , Glorieux
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Periodic Orbits near equilibria
Communications on Pure and Applied Mathematics, 2010AbstractLyapunov, Weinstein, and Moser obtained remarkable theorems giving sufficient conditions for the existence of periodic orbits emanating from an equilibrium point of a differential system with a first integral. Using averaging theory, we establish a similar result for a differential system without assuming the existence of a first integral.
Barreira, Luis +2 more
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STABILIZING HIGHER PERIODIC ORBITS
International Journal of Bifurcation and Chaos, 1994In this paper, we consider stabilization of chaotic dynamical systems onto higher periodic orbits. We give a necessary and sufficient condition for using local linear state feedback control for this purpose. The control is achieved using small, bounded perturbations, and the method proposed is shown to be effective even in the presence of relatively ...
Paskota, M., Mees, A. I., Teo, K. L.
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Normal Form Invariants Around Spin-Orbit Periodic Orbits
Celestial Mechanics and Dynamical Astronomy, 2000The authors consider an oblate satellite orbiting a central planet with \(T_{\text{rev}}\) the period of revolution. The satellite rotates about an internal spin axis with rotational period \(T_{\text{rot}}\). A spin-orbit resonance occurs when the ratio \(T_{\text{rev}}/T_{\text{rot}}\) is a rational number.
CELLETTI, ALESSANDRA, Falcolini, C.
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Periodic Orbits Near Homoclinic Orbits
1982It is known that the orbit-structure of a dynamical system near a homoclinic orbit γ is extremely complicated. However, it is only recently that this complicated structure has begun to be understood. It has been shown (under some hypotheses) that, near γ there are infinitely many long periodic orbits. The flow, near γ, admits a singular Poincare map o:
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1994
An intensively used method for finding periodic orbits is Newton’s method and variants thereof. We describe Newton’s method and the Quasi-Newton method later in this section. Newton→s method uses the initialization point y1, marked by the small cross, as its initial point.
Helena E. Nusse +2 more
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An intensively used method for finding periodic orbits is Newton’s method and variants thereof. We describe Newton’s method and the Quasi-Newton method later in this section. Newton→s method uses the initialization point y1, marked by the small cross, as its initial point.
Helena E. Nusse +2 more
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1994
As a parameter of a map is varied, periodic orbits are often seen to appear and shift in position and perhaps period double or blink out of existence. The orbit-following capability is for tracing their behavior as a parameter is varied. The orbit following routine runs for two dimensional maps, including for example the time-2π maps of periodically ...
Helena E. Nusse +2 more
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As a parameter of a map is varied, periodic orbits are often seen to appear and shift in position and perhaps period double or blink out of existence. The orbit-following capability is for tracing their behavior as a parameter is varied. The orbit following routine runs for two dimensional maps, including for example the time-2π maps of periodically ...
Helena E. Nusse +2 more
openaire +1 more source