Hojman, S. A., & Asenjo, F. A. (2020). Phenomenological dynamics of COVID19 pandemic: Metaanalysis for adjustment parameters. Chaos, 30(10), 12 pp.
Abstract: We present a phenomenological procedure of dealing with the COVID19 (coronavirus disease 2019) data provided by government health agencies of 11 different countries. Usually, the exact or approximate solutions of susceptibleinfectedrecovered (or other) model(s) are obtained fitting the data by adjusting the timeindependent parameters that are included in those models. Instead of that, in this work, we introduce dynamical parameters whose timedependence may be phenomenologically obtained by adequately extrapolating a chosen subset of the daily provided data. This phenomenological approach works extremely well to properly adjust the number of infected (and removed) individuals in time for the countries we consider. Besides, it can handle the subepidemic events that some countries may experience. In this way, we obtain the evolution of the pandemic without using any a priori model based on differential equations.

MontalvaMedel, M., Rica, S., & Urbina, F. (2020). Phase space classification of an Ising cellular automaton: The Q2R model. Chaos Solitons Fractals, 133, 14 pp.
Abstract: An exact classification of the different dynamical behaviors that exhibits the phase space of a reversible and conservative cellular automaton, the socalled Q2R model, is shown in this paper. Q2R is a cellular automaton which is a dynamical variation of the Ising model in statistical physics and whose space of configurations grows exponentially with the system size. As a consequence of the intrinsic reversibility of the model, the phase space is composed only by configurations that belong to a fixed point or a cycle. In this work, we classify them in four types accordingly to well differentiated topological characteristics. Three of them which we call of type SI, SII, and SIII share a symmetry property, while the fourth, which we call of type AS does not. Specifically, we prove that any configuration of Q2R belongs to one of the four previous types of cycles. Moreover, at a combinatorial level, we can determine the number of cycles for some small periods which are almost always present in the Q2R. Finally, we provide a general overview of the resulting decomposition of the arbitrary size Q2R phase space and, in addition, we realize an exhaustive study of a small Ising system (4 x 4) which is thoroughly analyzed under this new framework, and where simple mathematical tools are introduced in order to have a more direct understanding of the Q2R dynamics and to rediscover known properties like the energy conservation. (C) 2020 Elsevier Ltd. All rights reserved.

Rica, S. (2009). Analytical And Numerical Elements Of A Supersolid Model. Int. J. Bifurcation Chaos, 19(8), 2783–2800.
Abstract: In this article, the main properties of a model of supersolid in the frame of a GrossPitaevskii equation is reviewed. It was developed mainly by the author with Pomeau, Josserand and Sepulveda. Emphasis is placed on the numerical details and tools that are absent in our previous publications and maybe useful for authors who are eventually interested in the model. The model exhibits superfluid properties like nonclassical moment of inertia at T = 0K, quantized vortices and persistent currents without the presence of defects, moreover, only a transient flow is allowed by defects, akin to plastic flow in ordinary solids.

Ruivo, E. L. P., MontalvaMedel, M., de Oliveira, P. P. B., & Perrot, K. (2018). Characterisation of the elementary cellular automata in terms of their maximum sensitivity to all possible asynchronous updates. Chaos Solitons Fractals, 113, 209–220.
Abstract: Cellular automata are fullydiscrete dynamical systems with global behaviour depending upon their locally specified state transitions. They have been extensively studied as models of complex systems as well as objects of mathematical and computational interest. Classically, the local rule of a cellular automaton is iterated synchronously over the entire configuration. However, the question of how asynchronous updates change the behaviour of a cellular automaton has become a major issue in recent years. Here, we analyse the elementary cellular automata rule space in terms of how many different onestep trajectories a rule would entail when taking into account all possible deterministic ways of updating the rule, for one time step, over all possible initial configurations. More precisely, we provide a characterisation of the elementary cellular automata, by means of their onestep maximum sensitivity to all possible update schedules, that is, the property that any change in the update schedule causes the rule's onestep trajectories also to change after one iteration. Although the onestep maximum sensitivity does not imply that the remainder of the timeevolutions will be distinct, it is a necessary condition for that. (C) 2018 Elsevier Ltd. All rights reserved.

Soto, P. C., Cartes, C., Davies, T. P., Olivari, J., Rica, S., & VogtGeisse, K. (2020). The anatomy of the 2019 Chilean social unrest. Chaos, 30(7), 14 pp.
Abstract: We analyze the 2019 Chilean social unrest episode, consisting of a sequence of events, through the lens of an epidemiclike 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 welldefined pattern already observed in various public disorder episodes in other countries since the 1960s. Although the epidemiclike 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.
