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A precise theoretical investigation has been made on dust-acoustic (DA) waves(DAWs) in a four components dusty plasma medium having inertial warm adiabaticdust grains and inertialess $q$-distributed electrons as well as isothermalions and positrons. The nonlinear and dispersive parameters of the nonlinearSchr\"{o}dinger equation (NLSE), which develops by using reductiveperturbations technique, have been used to recognize the stable and unstableparametric regions of the DAWs as well as associated DA rogue waves (DARWs) inthe unstable parametric regime of the DAWs. The effects of the light positronsand massive dust grains in determining the amplitude and width of the DARWsassociated with DAWs are examined. The findings of our present investigationmay be useful for understanding different nonlinear electrostatic phenomena inboth space and laboratory plasmas.

Dust-acoustic rogue waves in an electron-positron-ion-dust plasma medium