Asymmetric Singularly Degenerate Heteroclinic Cycles

Although the axis-symmetric singularly degenerate heteroclinic cycles with nearby bifurcated axis-symmetric Lorenz-like attractors in axis-symmetric Lorenz-like system family were intensively studied in past decades, the scenario with asymmetric cycles has not been investigated. This paper revisits a simple Lorenz-like system, and illustrates asymmetric singularly degenerate heteroclinic cycles with nearby bifurcated asymmetric Lorenz-like attractors. In addition, it is proved that there exists a pair of asymmetric heteroclinic orbits to stable origin, and a pair of unstable and stable nontrivial asymmetric equilibria, in contrast to the axis/centro-symmetric ones to the unstable origin and a pair of stable nontrivial axis/centro-symmetric equilibria in most reported Lorenz-like systems. Moreover, this system casts a mirror image of the aforementioned dynamics from the parameter [Formula: see text] to d.