A ratio-dependent food chain model and its applications to biological control

Hsu, Sze Bi; Hwang, Tzy Wei; Kuang, Yang

doi:10.1016/s0025-5564(02)00127-x

Cited by 145 publications

(71 citation statements)

References 37 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Another popular explanation is that the stochastic forces are ubiquitous and when they are accounted in mathematical models, then the instability of E 0 may be lost. A more recent and intriguing explanation is that in the limiting scenarios when searching time is very small (like in a small island, or fragmented small patches), our functional responses can be approximated by the so-called ratio-dependent functional responses [10,14,15]. For such functionals, the origin can indeed be an attractor.…”

Section: Rabbits Have Strong Direct Effect On Birdsmentioning

confidence: 99%

Rabbits killing birds revisited

Zhang

Fan

Kuang

2006

Mathematical Biosciences

Self Cite

View full text Add to dashboard Cite

Section: Rabbits Have Strong Direct Effect On Birdsmentioning

confidence: 99%

Rabbits killing birds revisited

Zhang

Fan

Kuang

2006

Mathematical Biosciences

Self Cite

View full text Add to dashboard Cite

“…The model can take various forms depending on the specific choices of infection mechanisms and the predator functional responses. Appropriately formulated, these models shall be able to generate rich extinction dynamics such as the one documented in Hsu et al (2002). An example of such models with prey-dependent functional response may take the form Here x is the resource that interacts with pest.…”

Section: Instead It May Simply Drive the Host To Extinction (Whenmentioning

confidence: 99%

Deterministic extinction effect of parasites on host populations

Hwang

Kuang²

2003

Journal of Mathematical Biology

Self Cite

View full text Add to dashboard Cite

Abstract.Experimental studies have shown that parasites can reduce host density and even drive host population to extinction. Conventional mathematical models for parasite-host interactions, while can address the host density reduction scenario, fail to explain such deterministic extinction phenomena. In order to understand the parasite induced host extinction, Ebert et al. (2000) formulated a plausible but ad hoc epidemiological microparasite model and its stochastic variation. The deterministic model, resembles a simple SI type model, predicts the existence of a globally attractive positive steady state. Their simulation of the stochastic model indicates that extinction of host is a likely outcome in some parameter regions. A careful examination of their ad hoc model suggests an alternative and plausible model assumption. With this modification, we show that the revised parasite-host model can exhibit the observed parasite induced host extinction. This finding strengthens and complements that of Ebert et al. (2000), since all continuous models are likely break down when all population densities are small. This extinction dynamics resembles that of ratio-dependent predator-prey models. We report here a complete global study of the revised parasite-host model. Biological implications and limitations of our findings are also presented.

show abstract

“…There are several researchers (cf. [9,11,13,15,16,17,22,24]) who have concerned about the ecological systems with three and more species like system (1.2) to understand complex dynamical behaviors of ecological systems in the real world. Especially, the authors in [17] proposed a prey-predator model with two-type functional response and impulsive biological control by adding impulsive biological control strategy to the above system and investigated the existence of an asymptotically stable prey-free periodic solution under some conditions and established the permanence conditions for the impulsive system.…”

Section: Introductionmentioning

confidence: 99%

On the Dynamical Behavior of a Two-Prey One-Predator System with Two-Type Functional Responses

Baek

2013

Kyungpook mathematical journal

View full text Add to dashboard Cite

Abstract. In the paper, a two-prey one-predator system with defensive ability and Holling type-II functional responses is investigated. First, the stability of equilibrium points of the system is discussed and then conditions for the persistence of the system are established according to the existence of limit cycles. Numerical examples are illustrated to attest to our mathematical results. Finally, via bifurcation diagrams, various dynamic behaviors including chaotic phenomena are demonstrated.

show abstract

A ratio-dependent food chain model and its applications to biological control

Cited by 145 publications

References 37 publications

Rabbits killing birds revisited

Rabbits killing birds revisited

Deterministic extinction effect of parasites on host populations

On the Dynamical Behavior of a Two-Prey One-Predator System with Two-Type Functional Responses

Contact Info

Product

Resources

About