Extending the Biswas--Chatterjee--Sen model with nonconformists and inflexibles

Originally, the Biswas--Chatterjee--Sen model was shown to exhibit an order/disorder phase transition for a sufficiently large number of negative interactions among actors. In this paper, the model is extended by the existence of anticonformists and inflexibles. Anticonformists are actors who define themselves in opposition to the group and may intentionally reject what most people accept, while inflexibles are those who do not change their opinions at all. Both discrete and continuous opinions are considered. With direct Monte Carlo simulations and mean-field calculations, we check the influence of fractions of anticonformists and inflexibles on the mean opinion in the system. With the mean-field calculations, we identify ranges of fractions of anticonformists where an ordered phase of the system is available. The results of the mean-field calculations perfectly match the results of the Monte Carlo simulations. We consider inflexibles adhered: (i) to extreme opinions; (ii) to specific opinions, and (iii) chosen independently of their initial opinion. For inflexibles adhered to specific and extreme opinions, they play a role of an effective bias suppressing the disordered phase in the system. The qualitative results of introducing anticonformists (inflexibles) in various ways (discrete/continuous opinions and annealed/quenched disorder) are roughly the same. However, for the model extended by inflexibles, we can observe a systematic shift of the mean order parameter to its higher values for quenched disorder compared with annealed disorder. On the other hand, for anticonformists modeled with a continuous space of opinions, we can observe a systematic shift of the mean order parameter to its higher values compared with the discrete space of opinions.