The Yellow Vests Movement - a case of long transient dynamics?

Abstract

Understanding the dynamics of protests and social unrest is important in order to ensure a stable, sustainable development of the society. Mathematical models of social dynamics have been increasingly recognised as a powerful research tool in achieving this goal. Here, motivated by the fact that the dynamics of the ongoing Yellow Vest Movement in France exhibit anomalously long duration (currently it is in 30th week), we explore whether this can be a result of a dynamical systems phenomenon known as long transients. To this end, we build and study a hierarchy of mathematical models describing the "population dynamics" of the movement, i.e. how the number of protesters changes with time. We show that in these models long transients appear via two roots: via a ghost attractor and via an interaction of the slow and fast dynamics. We demonstrate that long transients are also present in some earlier models of social protests. Interestingly, our models predict that the Yellow Vest Movement should end abruptly by, at the latest, mid-summer 2019 without any interference from the French government. More generally, we argue that long transients are a generic feature of dynamical models describing social processes in the same way as they are in models of physical, ecological, and evolutionary systems.

Modelling Population Dynamics of Social Protests in Time and Space: The Reaction-Diffusion Approach

“…e.g., see [37,38]. Estimate (17) obtained by linearizing the system (12) and (13) therefore coincides with the speed of the travelling front in a scalar reaction-diffusion equation with the generalized logistic growth [42,43]. However, the expression (17) appears to be in bad disagreement with numerical results predicting a value considerably less than was obtained in the simulations, e.g., two instead of 3.1 for the parameters of Figure 8.…”

“…However, the expression (17) appears to be in bad disagreement with numerical results predicting a value considerably less than was obtained in the simulations, e.g., two instead of 3.1 for the parameters of Figure 8. Even worse, it does not in any way predict the dependence of the speed on parameter values: for instance, for = 0.1 Expression (17) gives c ≈ 0.63, whilst the actual value is about 2.6. A more careful look readily reveals the reason for this disagreement: as a matter of fact, Expression (17) is hardly relevant at all as its validity is limited to the case where the growth function is convex [42,43], whilst in our case, it is not (see Figure 12).…”

“…Figure 2 shows the solutions obtained for different values of m 0 and m 1 and other parameters chosen as 0 = 0.1, = 3, a = 146, h = 35, and b = 0.01. (We mention here that our choice of parameter values was not entirely random or hypothetical: it was shown in [17] that, with this parameter set, Model (1)-(5) provided a good description of the Yellow Vests protests.) We therefore observe that there are solution properties that are rather robust to parameter variation.…”

“…A more specific question is: How different can the dependence of the protester number on time be in spatial and non-spatial models for equivalent parameter values? Our paper intends to bridge this gap partially by considering a spatial extension of two non-spatial models recently developed in [17]. We will show that the dynamics of the spatial models can be qualitatively different, e.g., predicting the growth in the protester number for the parameter values where the non-spatial models predict decay.…”

“…The models range from relatively simple, allowing only for some basic feature of the phenomenon [3], to more complicated ones that take into account more details such as, for instance, heterogeneity of social norms and behavioural responses [9,15]. The case studies include a few well known events such as the Russian revolution of 1905-1907 [1], the French riots of 2005 [13], the London riots of 2011 [9], the Arab Spring [16], and the Yellow Vest Movement in 2018-2019 [17], in particular aiming to describe the intensity and timing of the unrest and to analyse the processes and mechanisms involved.…”