The saddle-node-transcritical bifurcation in a population model with constant rate harvesting

Saputra, Kie Van Ivanky; Quispel, G.

doi:10.3934/dcdsb.2010.14.233

Cited by 13 publications

(5 citation statements)

References 18 publications

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“…In (Saputra et al, 2010) the unfolding of two different types (one or two zero eigenvalues) of tangent-transcritical T-TC bifurcations are discussed. In (van Voorn and Kooi, 2013) a one zero eigenvalue example was analyzed.…”

Section: Transcritical-zero-hopf-hopf Bifurcationmentioning

confidence: 99%

Ecoepidemic models with prey group defense and feeding saturation

Gimmelli

Kooi

Venturino

2015

Ecological Complexity

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Section: Transcritical-zero-hopf-hopf Bifurcationmentioning

confidence: 99%

Ecoepidemic models with prey group defense and feeding saturation

Gimmelli

Kooi

Venturino

2015

Ecological Complexity

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“…is sufficient to qualitatively capture all the regimes predicted by the full model for any k. A similar normal form was proposed in [42] to describe the interaction of TC and SN bifurcations in an extended Lotka-Volterra model. The normal form is obtained through an expansion of R(p) given by Eq.…”

Section: A Minimal Modelmentioning

confidence: 80%

Bifurcations in synergistic epidemics on random regular graphs

Taraskin¹,

Pérez‐Reche²

2019

J. Phys. A: Math. Theor.

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The role of cooperative effects (i.e. synergy) in transmission of infection is investigated analytically and numerically for epidemics following the rules of Susceptible-Infected-Susceptible (SIS) model defined on random regular graphs. Nonlinear dynamics are shown to lead to bifurcation diagrams for such spreading phenomena exhibiting three distinct regimes: non-active, active and bi-stable. The dependence of bifurcation loci on node degree is studied and interesting effects are found that contrast with the behaviour expected for non-synergistic epidemics.

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“…The influence of constant terms in the usual LV model with quadratic nonlinearities was investigated in Ref. [31] from a purely mathematical perspective, but in general inhomogeneous population competition models did not receive much attention in the past. Here, we analyze and apply the GLV model with a constant inhomogeneity to the case of the orthogonal switching of two-spot polariton patterns.…”

Section: B Inhomogeneous Case S >mentioning

confidence: 99%

Externally controlled Lotka-Volterra dynamics in a linearly polarized polariton fluid

Pukrop

Schumacher

2020

Phys. Rev. E

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Spontaneous formation of transverse patterns is ubiquitous in nonlinear dynamical systems of all kinds. An aspect of particular interest is the active control of such patterns. In nonlinear optical systems this can be used for all-optical switching with transistor-like performance, for example realized with polaritons in a planar quantum-well semiconductor microcavity. Here we focus on a specific configuration which takes advantage of the intricate polarization dependencies in the interacting optically driven polariton system. Besides detailed numerical simulations of the coupled light-field exciton dynamics, in the present paper we focus on the derivation of a simplified population competition model giving detailed insight into the underlying mechanisms from a nonlinear dynamical systems perspective. We show that such a model takes the form of a generalized Lotka-Volterra system for two competing populations explicitly including a source term that enables external control. We present a comprehensive analysis both of the existence and stability of stationary states in the parameter space spanned by spatial anisotropy and external control strength. We also construct phase boundaries in non-trivial regions and characterize emerging bifurcations. The population competition model reproduces all key features of the switching observed in full numerical simulations of the rather complex semiconductor system and at the same time is simple enough for a fully analytical understanding of the system dynamics. :1903.12534v1 [cond-mat.other] arXiv

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The saddle-node-transcritical bifurcation in a population model with constant rate harvesting

Cited by 13 publications

References 18 publications

Ecoepidemic models with prey group defense and feeding saturation

Ecoepidemic models with prey group defense and feeding saturation

Bifurcations in synergistic epidemics on random regular graphs

Externally controlled Lotka-Volterra dynamics in a linearly polarized polariton fluid

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