Catastrophe theory in the phenomenological description of the avalanche effect in dc-biased microwave HTSC transmission lines

Within the framework of the proposed generalization of the phenomenological model of a microwave nonlinear HTSC transmission line, the effects of direct current on the transmission line are studied. Taking into account the next term in the expansion of the nonlinear dependence of the resistance on current allows us to explain the anomalous dependence of the insertion loss on the input power level observed in the experiment at subcritical temperatures. An additional direct current through the microwave waveguide can lead to the appearance of a bifurcation region in the space of control parameters. This is manifested in the possibility of an abrupt change in the properties of the waveguide at the boundaries of this region and the transition of the HTSC waveguide to a strongly dissipative state. The qualitative correspondence of the properties of the generalized phenomenological model to the data of experimental studies of the HTSC coplanar waveguide is obtained.