External activation promoting consensus formation in the opinion model with interest decay

We put forward an opinion model that considers internal decay and external activation or deactivation. Agents may withdraw from the discussion, meanwhile, these inactive agents are likely to be motivated by active neighbors. In addition, external influence from outside circumstances is added to the population. We focus on the majority rule of opinion exchange. Our investigations reveal under the impact of external circumstances, the system evolves to different stable states. One opinion can finally be made dominant when the internal motivation is large sufficiently. However, without external activation, consensus is hardly reached in the system with interest decay.

► We present an opinion model considering internal decay and external influence.
► Under the external impact, the system evolves to different stable states.
► One opinion can finally be made dominant by increasing the internal motivation.
► Without external activation, consensus is hardly reached in the system with internal decay.
► Relaxation time depends on both activation and interest decay parameters.