Jorge Rebaza

Dynamics of prey threshold harvesting and refuge

The dynamics of a predator-prey model with continuous threshold prey harvesting and prey refuge is studied. One central question is how harvesting and refuge could directly affect the dynamics of the ecosystem, such as the stability properties of some coexistence equilibria and periodic solutions. Theoretical and numerical methods are used to investigate boundedness of solutions, existence of bionomic equilibria, as well as the existence and stability properties of equilibrium points and periodic solutions. Several bifurcations are also studied.

Analysis of predator–prey models with continuous threshold harvesting

Abstract We formulate an alternative form of threshold harvesting and investigate its properties within the framework of a predator–prey model. Our formulation accounts for economic constraints and is defined as a continuous harvesting function of the predator species. Theoretical and numerical analysis indicate that our formulation, which we call continuous threshold policy (CTP), can help improve undesirable behavior of the predator–prey ecosystem. Our study includes uniform boundedness of solutions, stability of equilibria and periodic orbits, bifurcations, and heteroclinic orbits.

Approximate controllability of semilinear impulsive strongly damped wave equation

Abstract Rothes fixed-point theorem is applied to prove the interior approximate controllability of a semilinear impulsive strongly damped wave equation with Dirichlet boundary conditions in the space Z 1/2 =D((-Δ) 1/2 )×L 2 (Ω)

On Accelerating the PageRank Computation

{Z_{1/2} = D((-\Delta )^{1/2}) \times L^{2}(\Omega )}

Dynamics of predator-prey models with refuge, harvesting and dispersal

, where Ω is a bounded domain in ℝn (n ≥ 1). Under some conditions we prove the following statement: For all open nonempty subsets ω of Ω the system is approximately controllable on [0,τ]

Dynamics of ratio-dependent Predator-Prey models with nonconstant harvesting

{[0, \tau ]}

Point-to-Periodic and Periodic-to-Periodic Connections

. Moreover, we exhibit a sequence of controls steering the nonlinear system from an initial state z0 to a neighborhood of the final state z1 at time τ>0

From a KKM theorem to Nash equilibria in L-spaces

{\tau >0}

Dynamics of transitions in population interactions

.

Erratum: Point-to-Periodic and Periodic-to-Periodic Connections

In this paper we consider the problem of computing the PageRank vector in an efficient way. By combining some of the existing techniques and different approaches, including the power method, linear systems, iterative aggregation/disaggregation, and matrix reorderings, we propose algorithms that decrease the number of iterations to reach the desired solution, thus accelerating convergence to the vector that contains the importance of web pages.