5 citations · 6 across the 9 of their papers we have counts for
9 papers
SIR model with random diffusion, reinfection, and random transmission: exponential attractors and spread of the disease
Tomás Caraballo, Javier López-de-la-Cruz, Alexandre N. Oliveira-Sousa +1
We introduce a stochastic SIR-type partial differential equation model incorporating random diffusion, reinfection, vital dynamics, and a randomly varying transmission rate. For th…
Minimal jointly uniform attractor for nonautonomous random dynamical systems
Pedro Catuogno, Alexandre do Nascimento Oliveira-Sousa, Paulo Ruffino
We introduce a notion of minimal uniform attractor for nonautonomous random dynamical systems, which depends jointly on time and on a random parameter. Several examples are provide…
invariant, stable and inertial manifolds for non-autonomous dynamical systems
Radosław Czaja, Piotr Kalita, Alexandre N. Oliveira-Sousa
We use the version of the Lyapunov--Perron method operating on individual solutions to investigate the existence of invariant manifolds for non-autonomous dynamical systems, focusi…
SIR models with vital dynamics, reinfection and randomness to investigate the spread of infectious diseases
Javier López-de-la-Cruz, Alexandre N. Oliveira-Sousa
We investigate SIR models with vital dynamics, reinfection, and randomness at the transmission coefficient and recruitment rate. Initially, we conduct an extensive analysis of the…
New notion of nonuniform exponential dichotomy with applications to the theory of pullback and forward attractors
Jose Antonio Langa, Rafael Obaya, Alexandre N. Oliveira-Sousa
In this work we study nonuniform exponential dichotomies and existence of pullback and forward attractors for evolution processes associated to nonautonomous differential equations…
Continuity and topological structural stability for nonautonomous random attractors
Tomás Caraballo, Alexandre N. Carvalho, José A. Langa +1
In this work, we study continuity and topological structural stability of attractors for nonautonomous random differential equations obtained by small bounded random perturbations…
A Unified Theory for Inertial Manifolds, Saddle Point Property and Exponential Dichotomy
Alexandre N. Carvalho, Phillipo Lappicy, Estefani M. Moreira +1
Inertial manifold theory, saddle point property and exponential dichotomy have been treated as different topics in the literature with different proofs. As a common feature, they a…
The effect of a small bounded noise on the hyperbolicity for autonomous semilinear differential equations
Tomás Caraballo, Alexandre N. de Carvalho, José A. Langa +1
In this work we study permanence of hyperbolicity for autonomous differential equations under nonautonomous random/stochastic perturbations. For the linear case, we study robustnes…
Permanence of nonuniform nonautonomous hyperbolicity for infinite-dimensional differential equations
Tomás Caraballo, Alexandre N. Carvalho, José Antonio Langa +1
In this paper, we study stability properties of nonuniform hyperbolicity for evolution processes associated with differential equations in Banach spaces. We prove a robustness resu…