A two-patch prey-predator model with food-gathering activity

Ghosh, Sujoy Kumar; Bhattacharyya, S.K.

doi:10.1007/s12190-010-0446-z

Cited by 4 publications

(7 citation statements)

References 46 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Recently, there has been increasing empirical and theoretical work on the non-random foraging movements of predators which often responses to prey-contact stimuli such as spatial variation in prey density [10,39], or different type of signals arising directly from prey [74]. See more related examples of mathematical models in [48,44,11,7,12,21,9,43,15,31,27,55]. Kareiva [40] provided a good review on varied mathematical models that deal with dispersal and spatially distributed populations and pointed out the needs of including non-random foraging movements in meta-population models.…”

Section: Discussionmentioning

confidence: 99%

“…Their study showed that the extension of the Holling time budget argument to movement has essential effects on the dynamics. By extending the model of [31], Ghosh and Bhattacharyya [15] formulated a similar two patch prey-predator model with density-independent migration in prey and density-dependent migration in the predator. Their study shows that several foraging parameters such as handling time, dispersal rate can have important consequences in stability of prey-predator system.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A two-patch prey-predator model with predator dispersal driven by the predation strength

Kang

Sasmal

Messan

2017

Mathematical Biosciences and Engineering

View full text Add to dashboard Cite

Foraging movements of predator play an important role in population dynamics of prey-predator systems, which have been considered as mechanisms that contribute to spatial self-organization of prey and predator. In nature, there are many examples of prey-predator interactions where prey is immobile while predator disperses between patches non-randomly through different factors such as stimuli following the encounter of a prey. In this work, we formulate a Rosenzweig-MacArthur prey-predator two patch model with mobility only in predator and the assumption that predators move towards patches with more concentrated prey-predator interactions. We provide completed local and global analysis of our model. Our analytical results combined with bifurcation diagrams suggest that: (1) dispersal may stabilize or destabilize the coupled system; (2) dispersal may generate multiple interior equilibria that lead to rich bistable dynamics or may destroy interior equilibria that lead to the extinction of predator in one patch or both patches; (3) Under certain conditions, the large dispersal can promote the permanence of the system. In addition, we compare the dynamics of our model to the classic two patch model to obtain a better understanding how different dispersal strategies may have different impacts on the dynamics and spatial patterns.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A two-patch prey-predator model with predator dispersal driven by the predation strength

Kang

Sasmal

Messan

2017

Mathematical Biosciences and Engineering

View full text Add to dashboard Cite

show abstract

“…В зарубежной литературе за ней закрепилось другое названиемодель Розенцвейга -Макартура с логистическим законом роста численности жертв и функциональным откликом по Холлингу II типа [22]. Модель (1) и ее модификации встречается у некоторых исследователей [17,18,25,26], которые, к сожалению, ограничиваются локальным анализом устойчивости и изучением условий однородного распределения особей по ареалу. Данное исследование концентрируется на случае неоднородного распределения, которое проявляется в сложных нелинейных эффектах, связанных с эволюцией периодических режимов, при которых сообщества оказываются несинхронными, либо демонстрируют частичную синхронизацию.…”

Section: модель динамик двух неидентичных связанных сообществunclassified

“…Другими словами, было показано, что при слабой связи (m < 0.01) синхронизация, фактически, возможна лишь для идентичных сообществ. В целом, перечисленные результаты хорошо согласуются с результатами других авторов [17,18,25,26]. Однако, дальнейшее исследование модели (2) показало, что слабо связанные неидентичные сообщества способны, по крайней мере, к частичной синхронизации именно в случае большой разницы между значениями смертности хищников.…”

Section: модель динамик двух неидентичных связанных сообществunclassified

Synchronization and Bursting Activity in the Model for Two Predator-Prey Systems Coupled By Predator Migration

Кулаков¹,

Kurilova²,

Frisman³

2019

Math.Biol.Bioinf.

View full text Add to dashboard Cite

The papers is devoted to a model for two non-identical predator-prey communities coupled by migration and characterized by logistic growth of prey and Holling type II functional response. The coupling is a predator migration at constant weak rate. The non-identity is the difference in the prey growth rates or predator mortalities in each patch. We studied the equilibrium states of model and scenarios of loss of their stability and emerge of complex periodic solutions. It was shown that in some domains of the parameter space there is a bursting activity which are that the dynamics of two communities contain segments of slowly resting dynamic (as part of a fast-slow cycle or canard) and regular bursts of spikes. In the resting part, the dynamics of the second community, as a rule, follow the slow changes in the first community, i.e. the dynamics in different patches are synchronous. But in the fast part there is only phase synchronization between the fast-slow cycle in first patch and bursts in second. We classified the scenarios of transition between different types of bursting activity by location spiking manifold and canard. These types differ not so much in size, shape or numbers of spikes as in the order of bursts emerge relative a slow-fast cycle. In a typical case the start of burst (divergent fast oscillations) coincides with the minimum numbers or quasi-extinction of prey in the first patch. After a rapid increase in the prey number in the first patch, diverging fluctuations give way to damped in the second patch. Such dynamics correspond to the rhombus-wave shape of spikes cluster. Another case is interesting, when the burst of spikes is formed after the full recovery of prey and with a certain predator number in the first patch. In this case, the spikes cluster takes the shape of a triangle-wave or a truncated rhombus-wave. It was shown that transitions between these types of bursts are accompanied by a change in the oscillation period and the degree of synchronization. Triangular-wave bursters correspond to complete synchronization of the predator dynamics in the resting part and rhomboid-wave correspond to antiphase synchronization. In the fast part with many spikes, communities are completely asynchronous to each other.

show abstract

“…For example, the work of (Fraser and Cerri, 1982;Hansson, 1991;Jánosi and Scheuring, 1997;Namba, 1980;Nguyen-Ngoc et al, 2012;Savino and Stein, 1989;Silva et al, 2001) explored the effects of dispersal on population dynamics of prey-predator models when local population density is a selecting factor for dispersal. The work of Huang and Diekmann (2001) and Ghosh and Bhattacharyya (2011) studied the population dynamics of a two patch model with dispersal in predator driving by local population density of prey through Holling searching-handling time budget argument. The work of Kareiva and Odell (1987) studied dynamics when the dispersal of predator is carried out due to the concentrated food resources.…”

Section: Introductionmentioning

confidence: 99%

A two patch prey-predator model with multiple foraging strategies in predator: Applications to insects

Messan

Kang

2017

Discrete &Amp; Continuous Dynamical Systems - B

View full text Add to dashboard Cite

We propose and study a two patch Rosenzweig-MacArthur prey-predator model with immobile prey and predator using two dispersal strategies. The first dispersal strategy is driven by the preypredator interaction strength, and the second dispersal is prompted by the local population density of predators which is referred as the passive dispersal. The dispersal strategies using by predator are measured by the proportion of the predator population using the passive dispersal strategy which is a parameter ranging from 0 to 1. We focus on how the dispersal strategies and the related dispersal strengths affect population dynamics of prey and predator, hence generate different spatial dynamical patterns in heterogeneous environment. We provide local and global dynamics of the proposed model. Based on our analytical and numerical analysis, interesting findings could be summarized as follow: (1) If there is no prey in one patch, then the large value of dispersal strength and the large predator population using the passive dispersal in the other patch could drive predator extinct at least locally. However, the intermediate predator population using the passive dispersal could lead to multiple interior equilibria and potentially stabilize the dynamics;(2) The large dispersal strength in one patch may stabilize the boundary equilibrium and lead to the extinction of predator in two patches locally when predators use two dispersal strategies; (3) For symmetric patches (i.e., all the life history parameters are the same except the dispersal strengths), the large predator population using the passive dispersal can generate multiple interior attractors; (4) The dispersal strategies can stabilize the system, or destabilize the system through generating multiple interior equilibria that lead to multiple attractors; and (5) The large predator population using the passive dispersal could lead to no interior equilibrium but both prey and predator can coexist through fluctuating dynamics for almost all initial conditions.

show abstract

A two-patch prey-predator model with food-gathering activity

Cited by 4 publications

References 46 publications

A two-patch prey-predator model with predator dispersal driven by the predation strength

A two-patch prey-predator model with predator dispersal driven by the predation strength

Synchronization and Bursting Activity in the Model for Two Predator-Prey Systems Coupled By Predator Migration

A two patch prey-predator model with multiple foraging strategies in predator: Applications to insects

Contact Info

Product

Resources

About