Calculation of the isocline for the fixed point with a specified argument of complex multipliers

This paper proposes a calculation method to obtain the location of the fixed point in given nonlinear discrete system when the argument of complex multipliers is specified. We can calculate an isocline corresponding to the specified argument, then the stability and instantaneous phase around the fixed point can be discussed. As an application, we also propose a new calculation method of NS bifurcation parameter values with the specified argument. In addition, cross points of a cusp in a periodic entrainment region and the NS bifurcation curve is identified by this application