arXiv subjects

Matheus C. Santos

Publications and source records attributed to Matheus C. Santos.

6 recordsLinked to original sources

arXiv2026

On the Structure and Stability of Boundary Mixed Steady States in Evolutionary Games on Networks

We study steady states of evolutionary games on networks in which some players adopt pure strategies while others play mixed strategies. We refer to these configurations as boundary mixed steady states. Such states arise naturally in structured populations and have no counterpart in the classical well-mixed setting. We introduce a relaxed equilibrium notion, called boundary Nash equilibrium, in which the Nash condition is imposed only on non-pure players. In two-strategy systems, this notion characterizes boundary mixed steady states, while this correspondence breaks down in higher dimensions. The stability of these states is governed by the interaction structure among mixed players. When mixed players do not interact, the system exhibits continua of equilibria. In contrast, any nontrivial interaction generically produces instability. In particular, boundary mixed steady states that are not fully degenerate are never asymptotically stable. Degeneracies are further linked to the rank properties of the underlying interaction. These results reveal a structural instability mechanism specific to networked replicator dynamics, highlighting a qualitative gap with respect to the classical well-mixed case and showing how network topology influences the local behavior of equilibria.

math.DS↗

arXiv2026

Final size of a structured SIRD Model with active-population force of infection

We consider a SIRD epidemic model for a population composed of two groups of individuals with asymmetric interactions, where the force of infection depends on the active (alive) population in each group, rather than on the total population, as in the classical formulation. We prove that the final state for susceptible individuals is always positive and characterize it as the unique fixed point of a map. We also relate the final size to the basic reproduction number and show that the final number of susceptibles decreases when transmission rates increase. Numerical simulations compare the active-population and classical two-group SIRD models, showing differences in final size and the occurrence of multiple epidemic waves. The convergence of the fixed point approach is also illustrated.

q-bio.PE↗

arXiv2023

Final size and partial distance estimate for the SEIRD model

In this paper we consider a SEIRD epidemic model for a population composed by two groups with asymmetric interaction. Given two sets of parameters for the model, we estimate the distance of the solutions for the second group based on the distance of solutions for the first one. We also study the final size of the epidemic for each group. We illustrate our results with the spread of coronavirus disease 2019 (COVID-19) pandemic in the New York County (USA) for the initial stage of the contamination, and in the the cities of Petrolina and Juazeiro (Brazil).

physics.soc-ph↗

arXiv2016

Displacement convexity for the entropy in semidiscrete nonlinear Fokker-Planck equations

The displacement $λ$-convexity of a nonstandard entropy with respect to a nonlocal transportation metric in finite state spaces is shown using a gradient flow approach. The constant $λ$ is computed explicitly in terms of a priori estimates of the solution to a finite-difference approximation of a nonlinear Fokker-Planck equation. The key idea is to employ a new mean function, which defines the Onsager operator in the gradient flow formulation.

math.AP↗

arXiv2016

Minimizing Movement for a Fractional Porous Medium Equation in a Periodic Setting

We consider a fractional porous medium equation that extends the classical porous medium and fractional heat equations. The flow is studied in the space of periodic probability measures endowed with a non-local transportation distance constructed in the spirit of the Benamou-Brenier formula. For initial periodic probability measures, we show the existence of absolutely continuous curves that are generalized minimizing movements associated to Rényi entropy. For that, we need to obtain entropy and distance properties and to develop a subdifferential calculus in our setting.

math.AP↗

arXiv2014

Existence and symmetry for elliptic equations in R^n with arbitrary growth in the gradient

We study the semilinear elliptic equation $Δu + g(x,u,Du) = 0$ in $\R^n$. The nonlinearities $g$ can have arbitrary growth in $u$ and $Du$, including in particular the exponential behavior. No restriction is imposed on the behavior of $g(x,z,p)$ at infinity except in the variable $x$. We obtain a solution $u$ that is locally unique and inherits many of the symmetry properties of $g$. Positivity and asymptotic behavior of the solution are also addressed. Our results can be extended to other domains like half-space and exterior domains. We give some examples.

math.AP↗