Dynamics of a non-autonomous ratio-dependent food chain model

A simple non-autonomous ratio-dependent food chain model is investigated. It is shown that the system is permanence, extinction, ultimate boundedness and globally asymptotic stability under some appropriate conditions. Moreover, by employing Mawhin's coincidence degree theory, some easily applicable criteria are established for the global existence of positive periodic solution of this model. (C) 2009 Elsevier Inc. All rights reserved.