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 nonconformists and inflexible. Nonconformists are actors who do not follow the original model rules, but in different ways do something opposite while inflexibles are those who do not change their opinions. Both discrete and continuous opinions are considered. With direct Monte Carlo simulations and mean-field calculations, we check the influence of fractions of nonconformists and inflexibles on the mean opinion in the system. With the mean-field calculations we identify ranges of fractions of nonconformists where 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 effective bias suppressing disorder phase in the system. The qualitative results of introducing nonconformists (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.