Dynamical mechanism behind ghosts unveiled in a map complexification

Complex systems such as ecosystems, electronic circuits, lasers or chemical reactions can be modelled by dynamical which typically experience bifurcations. Transients suffer extremely long delays at the vicinity of bifurcations and it is also known that these transients follow scaling laws bifurcation parameter gets closer value in deterministic systems. The mechanisms involved local are well-known. However, for saddle-node bifurcations, relevant dynamics after occur complex phase space. Hence, mechanism responsible associated inverse-square root law this better understood looking We approach complexify a simple ecological system undergoing bifurcation. discrete model describes biological with facilitation (cooperation) under habitat destruction species non-overlapping generations. study (as opposed to real) once has occurred. identify fundamental causing (called ghosts), given two repellers Such appear close real line, thus forming narrow channel new fixed points slow passage orbits, remains tangible numbers analytically provide relation between inverse square-root multipliers repellers. finally prove same phenomenon occurs more general i.e., non-necessarily polynomial, models.