“…The asymptotic analysis of the fifth Painlevé transcendent has been studied by many authors, including Andreev and Kitaev (1997a, 1997b, 2000, Zeng and Zhao (2016), Bryuno and Parus and Qin and Shang (2006), McLeod (1999a, 1999b), McCoy and Tang (1986a, 1986b, 1986c, and Jimbo (1982). However, the literature on the asymptotic behaviours of the fifth Painlevé transcendent concentrates on behaviours on the real line, often focusing on special behaviours or solutions, while we consider all solution behaviours for x ∈ C. For other mathematical results related to P V , see (Boelen et al, 2013;Shimomura, 2011;Kaneko and Ohyama, 2007;Sasaki, 2007;Clarkson, 2005;Lu and Shao, 2004;Gordoa et al, 2001a;2001b), while for applications in physics see (Jimbo et al, 1980;Dyson, 1995;Schief, 1994), and references therein.…”