What is single orbit dynamics

In dynamic systems, some nonlinearities generate special connection problems of non-Z2symmetric homoclinic and heteroclinic orbits. Such orbits are important for analyzing problems of global bifurcation and chaos. In this paper, a general analytical method, based on the undetermined Padé approximation method, is proposed to construct non-Z2symmetric homoclinic and heteroclinic orbits which are affected by nonlinearity factors. Geometric and symmetrical characteristics of non-Z2heteroclinic orbits are analyzed in detail. An undetermined frequency coefficient and a corresponding new analytic expression are introduced to improve the accuracy of the orbit trajectory. The proposed method shows high precision results for the Nagumo system (one single orbit); general types of non-Z2symmetric nonlinear quintic systems (orbit with one cusp); and Z2symmetric system with high-order nonlinear terms (orbit with two cusps). Finally, numerical simulations are used to verify the techniques and demonstrate the enhanced efficiency and precision of the proposed method.

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STABILITY ANALYSIS AND SIMULATION OF N-CLASS RETRIAL SYSTEM WITH CONSTANT RETRIAL RATES AND POISSON INPUTS

Asia Pacific Journal of Operational Research ◽

10.1142/s0217595914400028 ◽

2014 ◽

Vol 31 (02) ◽

pp. 1440002 ◽

Cited By ~ 10

Author(s):

K. AVRACHENKOV ◽

E. MOROZOV ◽

R. NEKRASOVA ◽

B. STEYAERT

Keyword(s):

Queueing System ◽

Stability Domain ◽

Single Server ◽

Retrial Queueing System ◽

Retrial Queueing ◽

Single Orbit ◽

Transmission Control Protocols ◽

Regenerative Approach ◽

The Stability ◽

Multi Access

In this paper, we study a new retrial queueing system with N classes of customers, where a class-i blocked customer joins orbit i. Orbit i works like a single-server queueing system with (exponential) constant retrial time (with rate [Formula: see text]) regardless of the orbit size. Such a system is motivated by multiple telecommunication applications, for instance wireless multi-access systems, and transmission control protocols. First, we present a review of some corresponding recent results related to a single-orbit retrial system. Then, using a regenerative approach, we deduce a set of necessary stability conditions for such a system. We will show that these conditions have a very clear probabilistic interpretation. We also performed a number of simulations to show that the obtained conditions delimit the stability domain with a remarkable accuracy, being in fact the (necessary and sufficient) stability criteria, at the very least for the 2-orbit M/M/1/1-type and M/Pareto/1/1-type retrial systems that we focus on.

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Role of host star variability in the detectability of planetary phase curves

Astronomy and Astrophysics ◽

10.1051/0004-6361/201834166 ◽

2019 ◽

Vol 621 ◽

pp. A44

Author(s):

D. Hidalgo ◽

R. Alonso ◽

E. Pallé

Keyword(s):

Effective Temperature ◽

Thermal Emission ◽

Total Duration ◽

Phase Curve ◽

Single Orbit ◽

Reflected Light ◽

Planetary Orbits ◽

Minimum Number ◽

Temperature Ranges ◽

Low Amplitude

Phase curves, or the change in observed illumination of the planet as it orbits around its host star, help us to characterize their atmospheres. However, the variability of the host star can make their detection challenging. The presence of starspots, faculae, flares, and rotational effects introduce brightness variations that can hide other flux variations related to the presence of an exoplanet: ellipsoidal variation, Doppler boosting, and a combination of reflected light and thermal emission from the planet. Here we present a study to quantify the effect of stellar variability on the detectability of phase curves in the optical. In the first stage we simulated ideal data, with different white noise levels, and with cadences and total duration matching a quarter of the Kepler mission. We performed injection and recovery tests to evaluate the minimum number of planetary orbits that need to be observed in order to determine the amplitude of the phase curve with an accuracy of 15%. We also evaluate the effect of a simplistic stellar variability signal with low amplitude in order to provide strong constraints on the minimum number of orbits needed under these ideal conditions. In the second stage we applied these methods to data from Q9 of the Kepler mission, known for its low instrumental noise. The injection and recovery tests are performed on a selected sample of the less noisy stars in different effective temperature ranges. Even for the shortest explored planet period of 1 day, we find that observing a single orbit of the planet fails to detect accurately more than 90% of the inserted amplitude. The best recovery rates, close to 48%, are obtained after 10 orbits of a 1 day period planet with the largest explored amplitude of 150 ppm. The temperature range of the host stars providing better recovery ratios is 5500 K < Teff < 6000 K. Our results provide guidelines to selecting the best targets in which phase curves can be measured to the greatest accuracy, given the variability and effective temperature of its host star, which is of interest for the upcoming TESS, CHEOPS, and PLATO space missions.

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