Positive periodic solutions for Lotka–Volterra systems with a general attack rate

Lois-Prados, Cristina; Precup, Radu

doi:10.1016/j.nonrwa.2019.103024

Cited by 12 publications

(7 citation statements)

References 10 publications

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“…To transform our problem in an operator form, we lay on the following popular proposition, formally borrowed here from [27].…”

Section: Preliminariesmentioning

confidence: 99%

“…The proof is straightforward. At this point we manipulate with a convenient approach, used for example by Lois-Prados & Precup in [27], to express the solution in an integral operator form. For another integral operator approach one can see Tsvetkov [38].…”

Section: Preliminariesmentioning

confidence: 99%

“…The role of cone K γ (ω) becomes clear from the following proposition, assembled essentially from [24] (see also [27], [38]).…”

Section: Preliminariesmentioning

confidence: 99%

“…Often the situation enables to include the operator methods of functional analysis (see e.g. Lois-Prados & Precup [27], Tsvetkov [38]). Looks like that Krasnoselskii has been the first who used systematically theory of topological degree to investigate positive solutions of the operator equations (see [24], [25]).…”

Section: Introductionmentioning

confidence: 99%

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Positive periodic solutions for periodic predator-prey systems of Leslie-Gower or Holling-Tanner type

Tsvetkov,

Angelova-Slavova

2020

Preprint

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In this paper, we consider periodic predator -prey systems of Leslie -Gower or Holling -Tanner type, assuming that the coefficients are continuous positive ω-periodic functions. We prove an existence of positive ωperiodic solutions by means of operator method in Banach spaces with cones. No constructive conditions are required for the coefficients, besides the positivity and periodicity. At the end we point out that the used approach can be applied with minor changes for proving the existence of positive ω-periodic solutions even in the case of certain delays.

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“…To transform our problem in an operator form, we lay on the following popular proposition, formally borrowed here from [27].…”

Section: Preliminariesmentioning

confidence: 99%

Section: Preliminariesmentioning

confidence: 99%

“…The role of cone K γ (ω) becomes clear from the following proposition, assembled essentially from [24] (see also [27], [38]).…”

Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Positive periodic solutions for periodic predator-prey systems of Leslie-Gower or Holling-Tanner type

Tsvetkov,

Angelova-Slavova

2020

Preprint

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“…Since then, many modifications and new models have been defined trying to adapt the peculiarities observed in the real world as faithfully as possible. Some of the most recent papers on this topic are, for example, [28], [31], [14], [47], and [40], which deal with theoretical questions, or [11] and [20], which focus on real world settings.…”

Section: Introductionmentioning

confidence: 99%

A predator-prey two-sex branching process

Gutiérrez¹,

Minuesa²

2019

Preprint

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In this paper, we introduce a two-sex controlled branching model to describe the interaction of predator and prey populations with sexual reproduction. This process is a two-type branching process, where the first type corresponds to the predator population and the second one to the prey population. While each population is described via a two-sex branching model, the interaction and survival of both groups is modelled through control functions depending on the current number of individuals of each type in the ecosystem. We provide necessary and sufficient conditions for the ultimate extinction of both species, the fixation of one of the species and the coexistence of both of them. Moreover, the description of the present predator-prey two-sex branching process on the fixation events can be performed in terms of the behaviour of a one-type two-sex branching process with a random control on the number of individuals, which is also introduced and analysed.

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Study of the Nonelementary Singular Points and the Dynamics Near the Infinity in Predator-Prey Systems

Diz-Pita,

Llibre,

Otero-Espinar

2023

Nonlinear Systems and Complexity

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Positive periodic solutions for Lotka–Volterra systems with a general attack rate

Cited by 12 publications

References 10 publications

Positive periodic solutions for periodic predator-prey systems of Leslie-Gower or Holling-Tanner type

Positive periodic solutions for periodic predator-prey systems of Leslie-Gower or Holling-Tanner type

A predator-prey two-sex branching process

Study of the Nonelementary Singular Points and the Dynamics Near the Infinity in Predator-Prey Systems

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