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 fixed point properties, and Zorns lemma. Also, sufficient 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-flows of the

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... ous system exhibit an asymptotically stable periodic solution which is globally attractive and trapped in the absorbing region.