Interdependent-Network Criticality without a Second Network: Cascading Collapse of the Joule-Coupled Insulator-Metal Transition in $VO_2$
When driven by a large enough electric field or current, the insulating state of vanadium dioxide ($VO_2$) typically collapses abruptly into the metallic state (the insulator-metal transition, IMT) following a brief incubation delay. These incubation delays, typically lasting microseconds or less, have been analyzed predominantly through macroscopic electro-thermal modeling, providing little statistical insight into the transition dynamics. Here, we investigate the electrically driven IMT in a two-dimensional $VO_2$ lattice and demonstrate that the material behaves as a complex, interdependent network despite being a single structural entity. Because metallic domains dissipate significantly more Joule heat than insulating regions, each switching event raises the Joule heating of the network, resulting in network dependency and triggering a cascading chain reaction. Combining time-resolved resistance measurements with a Joule-coupled resistor-network model and interdependent-network theory, we observe an abrupt (first-order) transition preceded by an anomalously long incubation plateau lasting thousands of seconds. During this metastable plateau, an effective branching factor of the switching activity approaches unity at criticality, and the plateau lifetime diverges with exponent $ζ=1/2$; the order parameter scales with exponent $β=1/2$. These signatures coincide with those predicted for interdependent networks, indicating that dissipative Joule coupling alone can drive mixed-order catastrophic cascades in a single-network correlated-oxide system.