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Motivated by some previous works of Rudra et al we set to explore thebackground dynamics when dark energy in the form of New Variable ModifiedChaplygin gas is coupled to dark matter with a suitable interaction in theuniverse described by brane cosmology. The main idea is to find out theefficiency of New variable modified Chaplygin gas to play the role of DE. As aresult we resort to the technique of comparison with standard dark energymodels. Here the RSII brane model have been considered as the gravity theory.An interacting model is considered in order to search for a possible solutionof the cosmic coincidence problem. A dynamical system analysis is performedbecause of the high complexity of the system . The statefinder parameters arealso calculated to classify the dark energy model. Graphs and phase diagramsare drawn to study the variations of these parameters and get an insight intothe effectiveness of the dark energy model. It is also seen that the backgrounddynamics of New Variable Modified Chaplygin gas is consistent with the latecosmic acceleration. After performing an extensive mathematical analysis, weare able to constrain the parameters of new variable modified Chaplygin gas as$m<n$ to produce the best possible results. Future singularities are studiedand it is found that the model has a tendency to result in such singularitiesunlike the case of generalized cosmic Chaplygin gas. Our investigation leads usto the fact that New Variable Modified Chaplygin gas is not as effective asother Chaplygin gas models to play the role of dark energy.

How effective is new variable modified Chaplygin gas to play the role of dark energy- A dynamical system analysis in RS II Brane model