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J. Bifurcation Chaos"],"published-print":{"date-parts":[[2025,5]]},"abstract":"<jats:p> 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. 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