Number Of Stable Orbits Research Articles

Dynamical Packing in the Habitable Zone: The Case of Beta CVn

Abstract Uncovering the occurrence rate of terrestrial planets within the habitable zone (HZ) of their host stars has been a particular focus of exoplanetary science in recent years. The statistics of these occurrence rates have largely been derived from transiting planet discoveries, and have uncovered numerous HZ planets in compact systems around M-dwarf host stars. Here we explore the width of the HZ as a function of spectral type, and the dynamical constraints on the number of stable orbits within the HZ for a given star. We show that, although the Hill radius for a given planetary mass increases with larger semimajor axis, the width of the HZ for earlier-type stars allows for more terrestrial planets in the HZ than late-type stars. In general, dynamical constraints allow ∼6 HZ Earth-mass planets for stellar masses ≳0.7M ⊙, depending on the presence of farther out giant planets. As an example, we consider the case of Beta CVn, a nearby bright solar-type star. We present 20 yr of radial velocities (RV) from the Keck/High Resolution Echelle Spectrometer (HIRES) and Automated Planet Finder (APF) instruments and conduct an injection-recovery analysis of planetary signatures in the data. Our analysis of these RV data rule out planets more massive than Saturn within 10 au of the star. These system properties are used to calculate the potential dynamical packing of terrestrial planets in the HZ and show that such nearby stellar targets could be particularly lucrative for HZ planet detection by direct imaging exoplanet missions.

On the Number of Coexisting Autowaves in the Chain of Coupled Oscillators

We consider a model of neuron complex formed by a chain of diffusion coupled oscillators. Every oscillator simulates a separate neuron and is given by a singularly perturbed nonlinear differential-difference equation with two delays. Oscillator singularity allows reduction to limit system without small parameters but with pulse external action. The statement on correspondence between the resulting system with pulse external action and the original oscillator chain gives a way to demonstrate that under consistent growth of the chain node number and decrease of diffusion coefficient we can obtain in this chain unlimited growth of its coexistent stable periodic orbits (buffer phenomenon). Numerical simulations give the actual dependence of the number of stable orbits on the diffusion parameter value.

From synchronization to multistability in two coupled quadratic maps

The phenomenology of a system of two coupled quadratic maps is studied both analytically and numerically. Conditions for synchronization are given and the bifurcations of periodic orbits from this regime are identified. In addition, we show that an arbitrarily large number of distinct stable periodic orbits may be obtained when the maps parameter is at the Feigenbaum period-doubling accumulation point. An estimate is given for the coupling strength needed to obtain any given number of stable orbits.