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Bifurcations and multistability on the May-Holling-Tanner predation model considering alternative food for the predators
| dc.contributor.author | González-Olivares, Eduardo | |
| dc.contributor.author | Arancibia-Ibarra, Claudio | |
| dc.contributor.author | Rojas, Alejandro | |
| dc.contributor.author | González-Yañez, Betsabé | |
| dc.date.accessioned | 2019-12-03T20:15:02Z | |
| dc.date.available | 2019-12-03T20:15:02Z | |
| dc.date.issued | 2019 | |
| dc.identifier.uri | http://repositorio.ucm.cl/handle/ucm/2471 | |
| dc.description.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 dividing 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. | es_CL |
| dc.language.iso | en | es_CL |
| dc.rights | Atribución-NoComercial-SinDerivadas 3.0 Chile | * |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/cl/ | * |
| dc.source | Mathematical Biosciences and Engineering, 16(5), 4274-4298 | es_CL |
| dc.subject | Predator prey model | es_CL |
| dc.subject | Bifurcation | es_CL |
| dc.subject | Limit cycle | es_CL |
| dc.subject | Separatrix curve | es_CL |
| dc.subject | Stability | es_CL |
| dc.title | Bifurcations and multistability on the May-Holling-Tanner predation model considering alternative food for the predators | es_CL |
| dc.type | Article | es_CL |
| dc.ucm.facultad | Facultad de Ciencias Básicas | es_CL |
| dc.ucm.indexacion | Scopus | es_CL |
| dc.ucm.indexacion | Isi | es_CL |
| dc.ucm.uri | www.aimspress.com/article/10.3934/mbe.2019213 | es_CL |
| dc.ucm.doi | doi.org/10.3934/mbe.2019213 | es_CL |
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