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Superperiodicity,chaos and coexisting orbits of ion-acoustic waves (IAWs) are studied in a multi-component plasma consisting of fluid ions,q-nonextensive cold and hot electrons and Maxwellian hot positrons.The significant impacts of the system parameters on superperiodic and nonlinear periodic IAWs are presented.Considering an external periodic perturbation various types of quasiperiodic and chaotic features for IAWs are studied in different parametric ranges through time series' plots,phase spaces and Lyapunov exponents.It has been observed that there exist some coexisting orbits for IAWs.Coexisting orbits for IAWs in a classical electronpositron-ion plasma system are reported.