This paper discusses the domain of attraction and its sensitivity for a class of chaotic attractors generated by using second-order linear systems with hysteresis-series. It is found that the domain of attraction of the chaotic attractors is determined by an unstable limit cycle. The chaotic dynamical behaviors are demonstrated by using the Poincaré map. The sensitivity of the domain of attract...

Time delayed feedback control is well known as a practical method for stabilizing unstable periodic orbits embedded in chaotic attractors. However, this control method still has an open problem of estimating domain of attraction for target unstable periodic orbits. In this paper, we numerically discuss the domain of attraction in Duffing systems under the control method. The disturbance to init...

A sub-model of multivariate regular variation called hidden regular variation facilitates more accurate estimation of joint tail probabilities in the presence of asymptotic independence. A related concept called hidden domain of attraction can sometimes offer similar estimation assistance in circumstances where hidden regular variation is absent. Examples and discussion illustrate strengths and...

Long branch attraction is a problem that afflicts phylogenetic methods and a procedure to detect a data set suffering from this problem is the long branch extraction method[1]. This method has been well cited and used by many authors for their analysis but no strong validation has been performed as to its accuracy. We performed such an analysis by an extensive search of the branch length search...

The domain of attraction of a given non-linear system constitutes a zone of safe operation that can avoid unnecessary operational restrictions. In this paper, an alternative approach to the estimation of the domain of attraction of a saturated linear system is presented. Given a system with m saturated control inputs, we show how to choose a linear difference inclusion (LDI) in such a way that ...

Estimation of the domain of attraction of a class of susceptible infectious removed susceptible (SIRS) epidemic models for varying-size population with constant immigration is investigated. On assumption that the disease-free equilibrium and the endemic equilibrium exist, the domain of attraction of epidemic model is estimated by using sum-of-squares optimization approach. An invariant subset o...