Effective transport barriers in the biquadratic nontwist map

Nontwist area-preserving maps violate the twist condition at specific orbits, resulting in shearless invariant curves that prevent chaotic transport. Plasmas and fluids with nonmonotonic equilibrium profiles may be described using nontwist systems, where even after these shearless curves breakup, effective transport barriers persist, partially reducing transport coefficients. Some nontwist systems present multiple shearless curves in phase space, increasing the complexity of transport phenomena, which have not been thoroughly investigated until now. In this work, we examine the formation of effective transport barriers in a nontwist area-preserving mapping with multiple shearless transport barriers. By quantifying the effectiveness of each transport barrier in phase space, we identify two scenarios where particular barriers dominate over others. Our results also reveal configurations where the interplay of two transport barriers creates regions in phase space with significant orbit trapping, influencing overall transport dynamics.