A predator prey model with age structure

Cushing, J. M.; Saleem, Muhammad

doi:10.1007/bf01832847

Cited by 109 publications

(56 citation statements)

References 13 publications

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“…We refer to Ruan and Xiao [38] for a detailed presentation of model (1.2) and an overview on this topic. We also refer to Cushing and Saleem [13] for a presentation of prey-predator systems with an age structure.…”

Section: (T)u (T)mentioning

confidence: 99%

Bogdanov–Takens bifurcation in a predator–prey model

Liu

Magal

Xiao

2016

Z. Angew. Math. Phys.

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Abstract. In this paper, we investigate a class of predator-prey model with age structure and discuss whether the model can undergo Bogdanov-Takens bifurcation. The analysis is based on the normal form theory and the center manifold theory for semilinear equations with non-dense domain combined with integrated semigroup theory. Qualitative analysis indicates that there exist some parameter values such that this predator-prey model has an unique positive equilibrium which is Bogdanov-Takens singularity. Moreover, it is shown that under suitable small perturbation, the system undergoes the Bogdanov-Takens bifurcation in a small neighborhood of this positive equilibrium.

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Section: (T)u (T)mentioning

confidence: 99%

Bogdanov–Takens bifurcation in a predator–prey model

Liu

Magal

Xiao

2016

Z. Angew. Math. Phys.

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“…However, it is also increasingly realized that time delays are not necessarily destabilizing (see, e.g., Cushing andSaleem, 1982 andHastings, 1983). Additionally, Saleem et al (1987) confirmed this previous finding by arguing that increasing (decreasing) time delays are not necessarily destabilizing (stabilizing).…”

Section: Delay Effects In Dynamic Logit Modelsmentioning

confidence: 92%

Impacts of Multiple‐Period Lags in Dynamic Logit Models

Nijkamp

Reggiani

1992

Geographical Analysis

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This paper will provide an introduction to a new field of research, viz the sensitivity of the solution trajectory of a dynamic logit model (belonging to the class of discrete choice models) in the light of a multi-period lag structure. It is well known from recent advances in the area of chaos and turbulence theory that the stability of a dynamic system is critically dependent on various factors, such as threshold values of parameters, initial conditions and also the lag structure. This paper aims to identify the consequences of different lag structures in dynamic logit models (including also dynamic spatial interaction models). Various simulation experiments will be used to show that the onset of instability of the solution trajectory tends to decrease as the number of time lags increases (depending also on the growt.h rate of the system) . Acknowledgement

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“…We would like to mention that switching of stabilities in delayed predator-prey models has been observed and studied in Cushing [25] and Cushing and Saleem [26].…”

Section: Theorem 22mentioning

confidence: 99%

On Nonlinear Dynamics of Predator-Prey Models with Discrete Delay

Ruan

2009

Math. Model. Nat. Phenom.

157

100

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Abstract. In this survey, we briefly review some of our recent studies on predator-prey models with discrete delay. We first study the distribution of zeros of a second degree transcendental polynomial. Then we apply the general results on the distribution of zeros of the second degree transcendental polynomial to various predator-prey models with discrete delay, including Kolmogorov-type predator-prey models, generalized Gause-type predator-prey models with harvesting, etc. Bogdanov-Takens bifurcations in delayed predator-prey models with nonmonotone functional response and in delayed predator-prey model with predator harvesting are also introduced.

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A predator prey model with age structure

Cited by 109 publications

References 13 publications

Bogdanov–Takens bifurcation in a predator–prey model

Bogdanov–Takens bifurcation in a predator–prey model

Impacts of Multiple‐Period Lags in Dynamic Logit Models

On Nonlinear Dynamics of Predator-Prey Models with Discrete Delay

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