Preface

Yang, Kehu

doi:10.1016/s0076-5392(08)62861-1

Cited by 247 publications

(354 citation statements)

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“…If this is so, then the pattern just described may repeat indefinitely (stable oscillations have been observed in the model (1), as mentioned in [20]) or the oscillations may die down as the population tends to a fixed point (see figure 1 and corollary 9.3 on page 163 of [28]). …”

Section: (Right) We Can Say That a Nicholson Birth Function B(n ) Ismentioning

confidence: 89%

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Perverse Consequences of Infrequently Culling a Pest

Terry

Gourley

2010

Bull. Math. Biol.

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There are potentially many situations in which creatures will be subject to infrequent but regular culling. In terms of controlling crop pests, some farmers may only be able to afford to apply pesticides occasionally. Alternatively, pesticides may be applied only occasionally to limit their unwelcome side effects, which include pesticide resistance, chemical poisoning of agricultural workers, and environmental degradation. In terms of conservation, some species (such as the red deer in the UK) may be culled occasionally to maintain balances within their ecosystem. However, in this paper we discover, as the culmination of an exploration of adult-stage culling of a creature with juvenile and adult life stages, that, in certain circumstances, regular but infrequent culling will, perversely, increase the average population of the creature.

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Section: (Right) We Can Say That a Nicholson Birth Function B(n ) Ismentioning

confidence: 89%

“…so that the long time average of N (t) is bounded by the long time average in the absence of culling (further information would be required to determine the actual dynamics of solutions of (22), but relevant results are known and can be found, for example, in Kuang [28]). …”

Section: Remarkmentioning

confidence: 99%

Perverse Consequences of Infrequently Culling a Pest

Terry

Gourley

2010

Bull. Math. Biol.

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“…Near the origin, where both species face the possibility of extinction, the predation in the prey-dependent form can be approximated by a linear form of the product of prey and predator densities, which is no match to the strong recruitment of prey from specific growth. In other words, time delay alone will not cause, nor prevent the mutual extinction of both species in both prey-dependent and ratio-dependent cases (as well as for the general predator-dependent cases) (Kuang(1993), Beretta and Kuang (1998)). Deterministic extinction of both species is an extreme outcome of the predatorprey interaction, but seems to become ever more frequent and worrisome.…”

Section: Discussionmentioning

confidence: 99%

Global analysis of the Michaelis-Menten-type ratio-dependent predator-prey system

Hsu

Hwang

Kuang³

2001

Journal of Mathematical Biology

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334

171

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Abstract. The recent broad interest on ratio-dependent based predator functional response calls for detailed qualitative study on ratio-dependent predator-prey differential systems. A first such attempt is documented in the recent work of Kuang and Beretta(1998), where Michaelis-Menten-type ratio-dependent model is studied systematically. Their paper, while contains many new and significant results, is far from complete in answering the many subtle mathematical questions on the global qualitative behavior of solutions of the model. Indeed, many of such important open questions are mentioned in the discussion section of their paper.Through a simple change of variable, we transform the Michaelis-Menten-type ratiodependent model to a better studied Gause-type predator-prey system. As a result, we can obtain a complete classification of the asymptotic behavior of the solutions of the MichaelisMenten-type ratio-dependent model. In some cases we can determine how the outcomes depend on the initial conditions. In particular, open questions on the global stability of all equilibria in various cases and the uniqueness of limit cycles are resolved. Biological implications of our results are also presented.

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“…As in the previous two figures, data from baseline simulation of DDE system is shown for comparison. (Chen et al, 1999b) and cell cycle (Busenberg and Tang, 1994), as well as in various other fields (Kuang, 1993;Murray, 2001).…”

Section: Discussionmentioning

confidence: 99%

The importance of an inter-compartmental delay in a model for human gastric acid secretion

Marino

Ganguli

Joseph

et al. 2003

Bulletin of Mathematical Biology

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In this work we re-examine an existing model of gastric acid secretion. The model is a 2-compartment model of the human stomach accounting for regions where relevant cells (D, G, ECL and parietal cells) and proteins and acid they secrete (somatostatin, gastrin, histamine, and gastric acid, respectively) are found. These proteins compose a positive and negative feedback system that controls the secretion of gastric acid by parietal cells. The original model consists of 18 ordinary differential equations and yields a stable 3-period limit cycle solution. We modify the existing model by introducing a delay into the system and assuming that the cell populations are in steady state over a short-time window (<300 h) and are able to reduce the system to an 8-equation delay differential equation model. In addition to demonstrating congruency between the two models, we also show that a similar stability is only reproducible when the delay in gastrin transport is approximately 30 min. This suggests that gastric acid secretion homeostasis likely depends strongly on the delay in gastrin transport from the antrum to the corpus.

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Preface

Cited by 247 publications

References 0 publications

Perverse Consequences of Infrequently Culling a Pest

Perverse Consequences of Infrequently Culling a Pest

Global analysis of the Michaelis-Menten-type ratio-dependent predator-prey system

The importance of an inter-compartmental delay in a model for human gastric acid secretion

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