This paper studies the Lorenz-family system which is known to establish a topological connection among the Lorenz, Chen and Lu¨ systems in the parametric space. The existence of S˘i’lnikov heterclinic orbits is proved using an undetermined coefficient method. As a consequence, the...

Synchronization phenomena, an emergent property in networks of interacting dynamical elements, are widely observed in nature, and have become the subject of intense research. Here we will investigate the synchronization rate problem in coupled limit-cycle and chaotic oscillators. Based on the...