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Stochastic bifurcations and coherencelike resonance in a self-sustained bistable noisy oscillator
(2010)
We investigate the influence of additive Gaussian white noise on two different bistable self-sustained oscillators: Duffing-Van der Pol oscillator with hard excitation and a model of a synthetic genetic oscillator. In the deterministic case, both oscillators are characterized with a coexistence of a stable limit cycle and a stable equilibrium state. We find that under the influence of noise, their dynamics can be well characterized through the concept of stochastic bifurcation, consisting in a qualitative change of the stationary amplitude distribution. For the Duffing-Van der Pol oscillator analytical results, obtained for a quasiharmonic approach, are compared with the result of direct computer simulations. In particular, we show that the dynamics is different for isochronous and anisochronous systems. Moreover, we find that the increase of noise intensity in the isochronous regime leads to a narrowing of the spectral line. This effect is similar to coherence resonance. However, in the case of anisochronous systems, this effect breaks down and a new phenomenon, anisochronous-based stochastic bifurcation occurs.
Interacting human activities underlie the patterns of many social, technological, and economic phenomena. Here we present clear empirical evidence from Short Message correspondence that observed human actions are the result of the interplay of three basic ingredients: Poisson initiation of tasks and decision making for task execution in individual humans as well as interaction among individuals. This interplay leads to new types of interevent time distribution, neither completely Poisson nor power-law, but a bimodal combination of them. We show that the events can be separated into independent bursts which are generated by frequent mutual interactions in short times following random initiations of communications in longer times by the individuals. We introduce a minimal model of two interacting priority queues incorporating the three basic ingredients which fits well the distributions using the parameters extracted from the empirical data. The model can also embrace a range of realistic social interacting systems such as e-mail and letter communications when taking the time scale of processing into account. Our findings provide insight into various human activities both at the individual and network level. Our analysis and modeling of bimodal activity in human communication from the viewpoint of the interplay between processes of different time scales is likely to shed light on bimodal phenomena in other complex systems, such as interevent times in earthquakes, rainfall, forest fire, and economic systems, etc.
This work generates, through a sample of numerical simulations of the restricted three-body problem, diagrams of semimajor axis and eccentricity which defines stable and unstable zones for particles in S-type orbits around Pluto and Charon. Since we consider initial conditions with 0 <= e <= 0.99, we found several new stable regions. We also identified the nature of each one of these newly found stable regions. They are all associated to families of periodic orbits derived from the planar circular restricted three-body problem. We have shown that a possible eccentricity of the Pluto-Charon system slightly reduces, but does not destroy, any of the stable regions.
Föhlisch wird in seinem Vortrag die großen Zukunftsthemen der Mensch streifen: Energie, Umwelt und Struktur der Materie. Die Komplexität ihrer elementaren Prozesse erfordert die komplementäre Betrachtung der damit verbundene Dimensionen von Energie, Zeit und Raum. Dies lässt sich inzwischen mit Synchrotronstrahlungsquellen in größter Präision darstellen.
Saturn's rings host two known moons, Pan and Daphnis, which are massive enough to clear circumferential gaps in the ring around their orbits. Both moons create wake patterns at the gap edges by gravitational deflection of the ring material (Cuzzi, J.N., Scargle, J.D. [1985]. Astrophys. J. 292, 276-290; Showalter, MR., Cuzzi, J.N., Marouf, E.A., Esposito, LW. [1986]. Icarus 66, 297-323). New Cassini observations revealed that these wavy edges deviate from the sinusoidal waveform, which one would expect from a theory that assumes a circular orbit of the perturbing moon and neglects particle interactions. Resonant perturbations of the edges by moons outside the ring system, as well as an eccentric orbit of the embedded moon, may partly explain this behavior (Porco, CC., and 34 colleagues [2005]. Science 307, 1226-1236; Tiscareno, M.S., Burns, J.A., Hedman, MM., Spitale, J.N., Porco, CC., Murray, C.D., and the Cassini Imaging team [2005]. Bull. Am. Astron. Soc. 37, 767; Weiss, J.W., Porco, CC., Tiscareno, M.S., Burns, J.A., Dones, L [2005]. Bull. Am. Astron. Soc. 37, 767; Weiss, J.W., Porco, CC., Tiscareno, M.S. [2009]. Astron. J. 138, 272-286). Here we present an extended non-collisional streamline model which accounts for both effects. We describe the resulting variations of the density structure and the modification of the nonlinearity parameter q. Furthermore, an estimate is given for the applicability of the model. We use the streamwire model introduced by Stewart (Stewart, G.R. [1991]. Icarus 94, 436-450) to plot the perturbed ring density at the gap edges. We apply our model to the Keeler gap edges undulated by Daphnis and to a faint ringlet in the Encke gap close to the orbit of Pan. The modulations of the latter ringlet, induced by the perturbations of Pan (Burns, J.A., Hedman, M.M., Tiscareno, M.S., Nicholson, P.D., Streetman, B.J., Colwell, J.E., Showalter, M.R., Murray, C.D., Cuzzi, J.N., Porco, CC., and the Cassini ISS team [2005]. Bull. Am. Astron. Soc. 37, 766), can be well described by our analytical model. Our analysis yields a Hill radius of Pan of 17.5 km, which is 9% smaller than the value presented by Porco (Porco, CC., and 34 colleagues [2005]. Science 307, 1226- 1236), but fits well to the radial semi-axis of Pan of 17.4 km. This supports the idea that Pan has filled its Hill sphere with accreted material (Porco, C.C., Thomas, P.C., Weiss, J.W., Richardson, D.C. [2007]. Science 318, 1602-1607). A numerical solution of a streamline is used to estimate the parameters of the Daphnis-Keeler gap system, since the close proximity of the gap edge to the moon induces strong perturbations, not allowing an application of the analytic streamline model. We obtain a Hill radius of 5.1 km for Daphnis, an inner edge variation of 8 km, and an eccentricity for Daphnis of 1.5 x 10(-5). The latter two quantities deviate by a factor of two from values gained by direct observations (Jacobson, R.A., Spitale, J., Porco, C.C., Beurle, K., Cooper, N.J., Evans, M.W., Murray, C.D. [2008]. Astron. J. 135, 261-263; Tiscareno, M.S., Burns, J.A., Hedman, M.M., Spitale, J.N., Porco, C.C., Murray, C.D., and the Cassini Imaging team [2005]. Bull. Am. Astron. Soc. 37, 767), which might be attributed to the neglect of particle interactions and vertical motion in our model.