Carlos Cartes

At the end of the year 2019, Chile and, most specifically, Santiago, its capital, went through a large number of episodes of public violence, lasting several months. The geographical distribution of the intensity of those episodes has been studied in several previous works. There it was found that the geographic disposition of the public transport network largely explained which places from Santiago suffered most of the activity. A more recent work found that daily commuting travel, together with an epidemiological model, reproduced the main features of Santiago’s rioting distribution. The travelers who participated in the public disorder were called commuter rioters. The present work uses that previous epidemiological model, incorporating the influence of the commuter’s income on it. It was found that income redistribution, a by-product of daily travel, changes the disorder’s spatial density, showing a better agreement with the observations than otherwise and improving this formulation as a tool for describing and predicting different riot outcomes.

We investigate the properties of time-dependent dissipative solitons for a cubic complex Ginzburg–Landau equation stabilized by nonlinear gradient terms. The separation of initially nearby trajectories in the asymptotic limit is predominantly used to distinguish qualitatively between time-periodic behavior and chaotic localized states. These results are further corroborated by Fourier transforms and time series. Quasiperiodic behavior is obtained as well, but typically over a fairly narrow range of parameter values. For illustration, two examples of nonlinear gradient terms are examined: the Raman term and combinations of the Raman term with dispersion of the nonlinear gain. For small quintic perturbations, it turns out that the chaotic localized states are showing a transition to periodic states, stationary states, or collapse already for a small magnitude of the quintic perturbations. This result indicates that the basin of attraction for chaotic localized states is rather shallow.

During the second half of October 2019, Chile, especially the capital city, Santiago, suffered from widespread violence and public and private infrastructure destruction. This work aims to expand an epidemiological non-local model that successfully described the French riots of 2005 to incorporate the topology of Santiago’s subway network and explain the reported distribution of rioting activity in the city. Although the model reproduced the disorders’ aggregated temporal evolution, it could not deliver results resembling the observed spatial distribution of activity on Santiago. The main reason for this failure can be attributed to the fact that the model lacks a population displacement mechanism, which seems vital to explain Santiago’s unrest episodes.

Social disturbances due to socioeconomic and political factors received media attention during 2019 in places like France, Hong Kong, Chile, Nigeria, Sudan, Haiti, and Lebanon. In October 2019, Chile saw massive demonstrations in the capital city of Santiago. The cost of damage to infrastructure during the first month of unrest was estimated at US$ 4.6 billion, and the cost to the Chilean economy was about US$ 3 billion, 1.1% of its Gross Domestic Product. This study analyzes how the topology of the public transport network affected the locations of the 2019 riots in Santiago. On average, we find a clear association between proximity to the subway network and riot density. This association is significant only in neighborhoods with residents in the highest and lowest income quartiles. As a result, when analyzing social unrest and the critical role of public transport, policymakers should also consider the crucial role of income.

We investigate properties of oscillatory dissipative solitons (DSs) in a cubic complex Ginzburg-Landau equation stabilized by nonlinear gradient terms. As a main result we find a transition to dissipative solitons with spatiotemporal disorder as a function of the diffusion coefficient. This transition proceeds via quasiperiodicity and shows incommensurate satellites next to the fundamental frequency and its harmonics indicating a possible route to localized spatiotemporal chaos. The transition back to oscillatory DSs follows a similar scenario.

Social disturbances due to socioeconomic and political factors were present in the media during 2019, including places like France, Hong Kong, Chile, Nigeria, Sudan, Haiti, and Lebanon. In October 2019, Chile saw massive demonstrations in the capital city of Santiago. As a result, the cost of damage to infrastructure during the first month of unrest is estimated at US$ 4.6 billion, and the cost to the Chilean economy was about US$ 3 billion, 1.1% of its Gross Domestic Product. This study aims to analyze how the topology of the public transport network affected the locations of the 2019 riots in Santiago. On average, we find a clear association between proximity to the subway network and riot density. This association is significant only in neighborhoods with residents in the highest and lowest income quartiles. When analyzing social unrest and the critical role of public transport, policymakers should consider the crucial role of income in the previous relationship.

We investigate the influence of spatially homogeneous multiplicative noise on propagating dissipative solitons (DSs) of the cubic complex Ginzburg-Landau equation stabilized by nonlinear gradient terms. Here we focus on the nonlinear gradient terms, in particular on the influence of the Raman term and the delayed nonlinear gain. We show that a fairly small amount of multiplicative noise can lead to a change in the mean velocity for such systems. This effect is exclusively due to the presence of the stabilizing nonlinear gradient terms. For a range of parameters we find a velocity change proportional to the noise intensity for the Raman term and for delayed nonlinear gain. We note that the dissipative soliton decreases the modulus of its velocity when only one type of nonlinear gradient is present. We present a straightforward mean field analysis to capture this simple scaling law. At sufficiently high noise strength the nonlinear gradient stabilized DSs collapse.

We analyze the 2019 Chilean social unrest episode, consisting of a sequence of events, through the lens of an epidemic-like model that considers global contagious dynamics. We adjust the parameters to the Chilean social unrest aggregated public data available from the Undersecretary of Human Rights and observe that the number of violent events follows a well-defined pattern already observed in various public disorder episodes in other countries since the 1960s. Although the epidemic-like models display a single event that reaches a peak followed by an exponential decay, we add standard perturbation schemes that may produce a rich temporal behavior as observed in the 2019 Chilean social turmoil. Although we only have access to aggregated data, we are still able to fit it to our model quite well, providing interesting insights on social unrest dynamics.