Internal-external stimulus competition in a system of interacting moving particles: Persuasion versus propaganda

We propose a general nonlinear analytical framework to study the effect of an external stimulus in the internal state of a population of moving particles. This novel scheme allows us to study a broad range of excitation transport phenomena. In particular, considering social systems, it gives insight of the spatial dynamics influence in the competition between propaganda (mass media) and convincement. By extending the framework presented by Terranova et al. [Europhys. Lett. 105, 30007 (2014)], we now allow changes in individual's opinions due to a reflection induced by mass media. The equations of the model could be solved numerically, and, for some special cases, it is possible to derive analytical solutions for the steady states. We implement computational simulations for different social and dynamical systems to check the accuracy of our scheme and to study a broader variety of scenarios. In particular, we compare the numerical outcome with the analytical results for two possible real cases, finding a good agreement. From the results, we observe that mass media dominates the opinion state in slow dynamics communities; whereas, for higher agent active speeds, the rate of interactions increases and the opinion state is determined by a competition between propaganda and persuasion. This difference suggests that kinetics can not be neglected in the study of transport of any excitation over a particle system.

Figure 1

One-dimensional representation of the populations $P_i$ with opinion states $i$. The arrows $R_i,r_i$ $(L_i,l_i)$ represent the fraction of agents changing its opinion to the right (left) due to persuasion $\left(R,L\right)$ or reflection $\left(r,l\right)$.

Figure 2

Stationary states as a function of the overall drift rate $C_c$. From the figure it is apparent that when persuasion and reflection dynamics are strongly biased, fundamentalist states predominate over the moderate ones. Slight biased dynamic permits the coexistence among the different degrees of opinions.

Figure 3

Steady-state agent populations $P_{A^{+}}$ (open symbols) and $P_{A^{-}}$ (closed symbols) as a function of the agents active speed. Lines correspond to steady-state analytical results obtained from solving Eq. (2).

Figure 4

Steady-state agent population as a function of the box length $L$ for $P_{A^{+}}$. Simulation data (symbols) and analytical stationary solutions of Eq. (2) for different values of $L$ (lines). The active speed is $v=0.05\mathrm{a}.\mathrm{u}.$ and the others parameters are given in Ref. [22].

Figure 5

Simulation data (symbols) and analytical stationary solutions of Eq. (2) (lines) for case 1 (fundamentalist do not reflect). The squares correspond to $P_{A^{+}}$ and the triangles correspond to $P_{A^{-}}$. For $P_{B^{+}}$ and $P_{B^{-}}$ the behavior is analogous.

Figure 6

Simulation data (symbols) and analytical steady-state solutions of Eq. (2) (lines) for the populations in case 2 (persuasion vs. reflection). In case $\left(a\right)$ the parameters are $r_i=6\times {10}^{-4}$ and $l_i=3\times {10}^{-4}$; in case $\left(b\right)$ are $r_i=6\times {10}^{-3}$ and $l_i=3\times {10}^{-3}$; and in case $\left(c\right)$ are $r_i=6\times {10}^{-2}$ and $l_i=3\times {10}^{-2}$.