In this paper, we study the dynamical modes of the modified noisy voter model. Inour model, the changes in the binary state (opinion) of the voters (agents) are causedby the avalanche-like dynamics of the threshold variables (tensors) assigned to them. Thesystem under study is considered as a scale-free network in which the nodes representelements (agents, voters) and the edges represent possible contacts between the elements.The structure of the links between voters is not static. Its temporal evolution is due to the“activity” of the agents. This property determines the probability that an agent is connectedto its nearest neighbors at a given time. Within the model, an agent that is not linked toneighbors can change its opinion to an opposite one, regardless of the opinions of other agents.A linked agent can copy the opinion of its neighbor during an avalanche process. Analyticallyand numerically, we show that the value of agents’ “activity” completely determines the modeof opinion dynamics. We derive a critical value of the “activity” at which there is a transitionbetween two dynamic regimes of the system. In the first case, the system switches between twoconsensus states. In the opposite case, the system tends to a state where opposing opinionscoexist and the system-averaged opinion is zero. We show that the analytical approachdescribes the behavior of the system qualitatively well.