ORCID Profile
0000-0002-5837-1571
Current Organisation
Universidad Católica del Maule
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Publisher: American Institute of Mathematical Sciences (AIMS)
Date: 2019
DOI: 10.3934/MBE.2019403
Abstract: In the ecological literature,many models for the predator-prey interactions have been well formulated but partially analyzed.Assuming this analysis to be true and complete,some authors use that results to study a more complex relationship among species (food webs).Others employ more sophisticated mathematical tools for the analysis,without further questioning.The aim of this paper is to extend,complement and enhance the results established in an earlier article referred to a modified Leslie-Gower model.In that work,the authors proved only the boundedness of solutions,the existence of an attracting set,and the global stability of a single equilibrium point at the interior of the first quadrant.In this paper,new results for the same model are proven,establishing conditions in the parameter space for which up two positive equilibria exist.Assuming there exists a unique positive equilibrium point,we have proved,the existence of:i) a separatrix curve Σ, iding the trajectories in the phase plane,which can have different
Publisher: MDPI AG
Date: 23-09-2022
DOI: 10.3390/MATH10193467
Abstract: This paper investigates the problem of control design for dc–dc converters, where the solution is especially suitable to address variations in the input voltage, a frequent situation in photovoltaic systems, and the problem of constant power load, where a nonlinear load is connected to the output of the converter. The proposed approach models the converters in terms of Linear Parameter-Varying (LPV) models, which are used to compute gain-scheduled robust gains. The synthesis conditions provide stabilizing controllers with an attenuation level of disturbances in terms of the H∞ norm. Moreover, the design conditions can also overcome pole locations to comply with physical application restrictions when ensuring transient performance. The validation of the controllers is made via simulation of the classical converters (buck, boost and buck-boost), showing that the proposed method is a viable and generalized control solution that works for all three converters, with guarantees of closed-loop stability and good performance.
Publisher: American Institute of Mathematical Sciences (AIMS)
Date: 2019
DOI: 10.3934/MBE.2019213
Abstract: In this paper a modified May-Holling-Tanner predator-prey model is analyzed, considering an alternative food for predators, when the quantity of prey i scarce. Our obtained results not only extend but also complement existing ones for this model, achieved in previous articles. The model presents rich dynamics for different sets of the parameter values it is possible to prove the existence of: (i) a separatrix curve on the phase plane iding the behavior of the trajectories, which can have different ω-limit this implies that solutions nearest to that separatrix are highly sensitive to initial conditions, (ii) a homoclinic curve generated by the stable and unstable manifolds of a saddle point in the interior of the first quadrant, whose break generates a non-infinitesimal limit cycle, (iii) different kinds of bifurcations, such as: saddle-node, Hopf, Bogdanov-Takens, homoclinic and multiple Hopf bifurcations. (iv) up to two limit cycles surrounding a positive equilibrium point, which is locally asymptotically stable. Thus, the phenomenon of tri-stability can exist, since simultaneously can coexist a stable limit cycle, joint with two locally asymptotically stable equilibrium points, one of them over the y-axis and the other positive singularity. Numerical simulations supporting the main mathematical outcomes are shown and some of their ecological meanings are discussed.
No related grants have been discovered for Alejandro Rojas.