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Author (up) Gonzalez-Olivares, E.; Gonzalez-Yanez, B.; Becerra-Klix, R.; Ramos-Jiliberto, R. pdf  doi
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  Title Multiple stable states in a model based on predator-induced defenses Type
  Year 2017 Publication Ecological Complexity Abbreviated Journal Ecol. Complex.  
  Volume 32 Issue Pages 111-120  
  Keywords Predator prey theory; Inducible defenses; Refuges; Stability; Separatrix  
  Abstract A large variety of antipredator defenses are exhibited by plants, animals and microbes in nature. A deep understanding of the dynamic consequences of prey responses to predation risk is essential for building a comprehensive theory of food webs. Here we present a simple classification of prey defenses based on the sensitivity of prey immunity to predation respect to abundances of prey and predators. Only three out of six defense types have been analytically studied in the context of predator-prey dynamics, which reveals a serious gap in our current knowledge of ecological interactions. In this study we present a mathematical analysis on a widely occurring type of prey defense whose behavior has not been established in exact terms. The study model considers prey whose average immunity to predators is enhanced by predator abundance. This case, known as inducible defenses, has been reported for a wide array of species. Our results reveal a rich dynamic behavior, in which the predator-prey system exhibits either one, two or three positive equilibrium points, with up to two attractors. Thus, inducible defenses constitute a mechanism that could drive alternative stable states even in very simple food web models. (C) 2017 Elsevier B.V. All rights reserved.  
  Address [Gonzalez-Olivares, Eduardo; Gonzalez-Yanez, Betsabe] Pontificia Univ Catolica Valparaiso, Av Brasil 2950, Valparaiso, Chile, Email: ejgonzal@ucv.cl;  
  Corporate Author Thesis  
  Publisher Elsevier Science Bv Place of Publication Editor  
  Language English Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 1476-945x ISBN Medium  
  Area Expedition Conference  
  Notes WOS:000418989900009 Approved  
  Call Number UAI @ eduardo.moreno @ Serial 825  
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Author (up) Vera-Damian, Y.; Vidal, C.; Gonzalez-Olivares, E. doi  openurl
  Title Dynamics and bifurcations of a modified Leslie-Gower-type model considering a Beddington-DeAngelis functional response Type
  Year 2019 Publication Mathematical Methods In The Applied Sciences Abbreviated Journal Math. Meth. Appl. Sci.  
  Volume 42 Issue 9 Pages 3179-3210  
  Keywords Beddington-DeAngelis functional response; Bogdanov-Takens bifurcation; homoclinic bifurcation; Hopf bifurcation; limit cycles; predator-prey model; stability  
  Abstract In this paper, a planar system of ordinary differential equations is considered, which is a modified Leslie-Gower model, considering a Beddington-DeAngelis functional response. It generates a complex dynamics of the predator-prey interactions according to the associated parameters. From the system obtained, we characterize all the equilibria and its local behavior, and the existence of a trapping set is proved. We describe different types of bifurcations (such as Hopf, Bogdanov-Takens, and homoclinic bifurcation), and the existence of limit cycles is shown. Analytic proofs are provided for all results. Ecological implications and a set of numerical simulations supporting the mathematical results are also presented.  
  Address [Vera-Damian, Yrina] Univ Adolfo Ibanez, Fac Ingn & Ciencias, Santiago, Chile, Email: edvera@alumnos.uai.cl  
  Corporate Author Thesis  
  Publisher Wiley Place of Publication Editor  
  Language English Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0170-4214 ISBN Medium  
  Area Expedition Conference  
  Notes WOS:000467275100016 Approved  
  Call Number UAI @ eduardo.moreno @ Serial 998  
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