Existence and Uniqueness of Positive Periodic Solution of an Extended Rosenzweig-MacArthur Model via Brouwer's Topological Degree

The necessary conditions for existence of periodic solutions of an Extended Rosenzweig-MacArthur model are obtained using Brouwer's degree. The forward invariant set is formulated to ensure the boundedness of the solutions, using Brouwers xed point properties, and Zornslemma. Also, sucient conditions for the existence of a unique positive periodic solution have been established using Barbalats lemma and Lyapunovs functional. Numerical responses show that, the phase-ows of the non-autonomous system exhibit an asymptotically stable periodic solution which is globally attractive and trapped in the absorbing region.