Thermal management of electronic devices has been a long-standing focal point of research in the area of heat transfer and two-phase flows. Many technologies have emerged to address the problems associated with thermal heating in these devices. Among several such cooling technologies, heat pipe technology has shown a promising potential solution to the heating problems. Pulsating heat pipes (PHPs) are very successful heat exchangers for high heat removal systems with small surface areas. Their miniature size with wickless structure and performance in different operating conditions make them a perfect candidate to use in space applications. The complexity involved in the thermodynamic processes makes it very hard to model the operating characteristics of the system. The absence of these operating characteristics prohibits the PHP to use in practical applications. Therefore, the fundamental problem lies in the understanding of the dynamics in the non-linear regime. Nonlinear stability analysis has been carried out to find the non-linear dynamical behavior of the system. A model explaining several thermodynamic processes has been employed for the analysis. The oscillatory behavior of the liquid slug is modeled similarly to the spring-mass system. The resultant system of non-linear differential equations, containing the conservation equations for the liquid slug and vapor plug separately, has been solved numerically using MATCONT. The analysis shows the transient behavior with a similar characteristic of the start-up conditions of reported work. The temperature profiles and associated flow rates have shown the possibility of a hop point in the parameter space.