# Joanna Toruniewska, RENOIR visitor to the Center presented a seminar entitled "The new constant of motion for coevolving voter model" hosted by Prof. Boleslaw K. Szymanski on October 11, 2018

Joanna Toruniewska, a RENOIR researcher from Warsaw Technological University in Poland visiting the NEST Center presented a seminar entitled "The new constant of motion for coevolving voter model" hosted by Prof. Boleslaw K. Szymanski on October 11, 2018

The talk focuses on the coevolving voter model in which a topology of the network changes in response to the voter dynamics on the network. In detail, nodes can change their state with probability (1-p) and links can rewire, with probability p, in order to connect nodes of the same state. We consider the process of reaching the final state in this model. We treat mean degree of nodes in different states as separate variables, which do not have to be equal. This allows to discuss the magnetization of nodes n and the magnetization of links m as potentially independent variables. Our studies show that in the active phase, both mean values of magnetization tend to the same value that depends on initial conditions. In a similar way mean degrees of spins up and spins down become equal. If the rewiring probability is above a critical value and the system separates into disconnected domains, the values of nodes and links magnetizations are not the same and final mean degrees of spins up and spins down can be different. Mean field calculation indicate that these two magnetizations are coupled and their linear combination is a statistical constant of motion: Λ≡(1-p)μm(t)+pn(t)=const, where μ is the mean node degree.