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Electro-magneto-active (EMA) polymers-based smart actuators suffer from electro-magneto-mechanical instability (EMMI) phenomena arising due to the positive feedback between the applied electric and magnetic fields and reduction in the polymer thickness. This work presents a theoretical investigation of EMMI phenomena of an EMA polymeric actuator in both static and DC dynamic modes of operation. A physics-based non-affine material model is adopted here for capturing the effect of the polymer chain entanglements and crosslinks on the instability phenomena. Simultaneously, a computationally efficient energy approach for obtaining the DC dynamic instability parameters is constructed, which depends on the energy balance at the position of maximal overshoot in an oscillation cycle. The findings from the current study illustrate the trends of variation in the deformation, electric field, and magnetic field at the onset of static and dynamic EMMI with the polymeric entanglements and crosslinks parameters. It is observed that large entanglements and crosslinks in polymer chains improve the stable operation travel range, which positively impacts the actuator performance. [ABSTRACT FROM AUTHOR]