Nonconservative kinetic exchange model of opinion dynamics with randomness and bounded confidence

The concept of a bounded confidence level is incorporated in a nonconservative kinetic exchange model of opinion dynamics model where opinions have continuous values is an element of [-1,1]. The characteristics of the unrestricted model, which has one parameter lambda representing conviction, undergo drastic changes with the introduction of bounded confidence parametrized by delta. Three distinct regions are identified in the phase diagram in the delta-lambda plane and the evidences of a first order phase transition for delta >= 0.3 are presented. A neutral state with all opinions equal to zero occurs for lambda <= lambda(c1) similar or equal to 2/3, independent of delta, while for lambda(c1) <= lambda <= lambda(c2) (delta) an ordered region is seen to exist where opinions of only one sign prevail. At lambda(c2) (delta), a transition to a disordered state is observed, where individual opinions of both signs coexist and move closer to the extreme values (+/- 1) as lambda is increased. For confidence level delta < 0.3, the ordered phase exists for a narrow range of lambda only. The line delta = 0 is apparently a line of discontinuity, and this limit is discussed in some detail.