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This work we prfesent the investigate stability of both liquid single phase limit for melting nanoparticle, heating liquid models. For the study we transform both modeles to Lienard equations. The associated Lyapunov function of both models are computed by using the Lyapunov direct method, the stability for both system are established, and these imply that the models are stable under the given initial and boundary conditions. Physically this means that the liquid and heating liquid nanoparticales system are stable in the plane. Finally we investigate the existence of limit cycles for both systems are found to be non-existent
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