In the study of dynamical systems, a homoclinic orbit is a path through phase space which joins a saddle equilibrium point to itself. More precisely, a homoclinic orbit lies in the intersection of …

Homoclinic and heteroclinic connections and intersections. In dynamical systems, a branch of mathematics, a homoclinic connection is a structure formed by the stable manifold and …

同宿轨道(homoclinic orbit)是指一条连续动态系统将平衡鞍点连接到自身的轨迹。 简单地说，同宿轨道存在于稳定于平衡点的稳定支路与非稳定支路的交点。

1998年1月15日 · This survey article reviews the theory and application of homoclinic orbits to equilibria in reversible continuous-time dynamical systems, where the homoclinic orbit and the …

A. For A = 0 there is a homoclinic connection from x= ˇto the equivalent version x= ˇ. For non-zero A we can consider the stroboscopic t = 2ˇ 1 map, which is now an autonomous two …

2025年3月7日 · Although scholars have proven the existence of a pair of homoclinic orbits to the origin, or a pair of heteroclinic orbits to the origin along with a pair of nontrivial equilibria in …

2020年6月5日 · If the saddle-node has a single homoclinic orbit $ \Gamma _ {0} $, then, generically, a unique limit cycle bifurcates from $ \Gamma _ {0} $, when the saddle-node …

2025年3月5日 · The homoclinic or heteroclinic orbits are general nonlinear phenomena in nature. For example, it often lies at the heart of what is termed bursting phenomena in mathematical …

2011年3月15日 · The paper provides a new series method, named scaling logarithm change series (SLS) method, to find homoclinic or heteroclinic orbits in continuous-time autonomous …

2025年2月17日 · In this work we intend to study homoclinic classes for some classes of flows. To this end we obtain analogous results those obtained by Hertz-Hertz-Tahzibi-Ures in the flow …