The role of space in stage-structured cannibalism with harvesting of an adult predator

Bhattacharyya, Joydeb; Pal, Samares

doi:10.1016/j.camwa.2013.05.011

Cited by 11 publications

(6 citation statements)

References 25 publications

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“…In this paper, by introducing ratio-dependent functional response for the growth of Parrotfish and Pterois volitans and by considering refuge protection for Parrotfish, we obtain results that justify the real-field observations. The effect of cannibalism is not clearly stated in [20,21], whereas, in [22] it is observed that higher rate of cannibalism induces oscillation around the positive equilibrium. Since [22] is studied by means of a single-species stage-structured model, it could not be evaluated from this paper whether cannibalism of Pterois volitans actually reduces predation pressure on Parrotfish.…”

Section: Introductionmentioning

confidence: 62%

“…Also, Hsu et al [19] observed that ratio-dependent predator-prey models exhibit complicated dynamics near the boundaries. Our mathematical model is a direct extension of the models studied in [20,21] under the assumption that algae is growing logistically and Parrotfish is growing on algae with a functional response which depends on the density of algae as well as Parrotfish. In our previous studies [22], it is observed that the system becomes oscillatory around the interior equilibrium when the invasion rate of Pterois volitans exceeds some certain critical threshold.…”

Section: Introductionmentioning

confidence: 99%

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Stage-Structured Cannibalism in a Ratio-Dependent System with Constant Prey Refuge and Harvesting of Matured Predator

Bhattacharyya

Pal

2016

Differ Equ Dyn Syst

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A four dimensional stage-structured ratio-dependent predator-prey model with constant prey refuge is proposed and analyzed to study the effect of predation and cannibalism of the organisms at the highest trophic level with harvesting. Our analysis leads to different thresholds in terms of the model parameters acting as conditions under which the organisms associated with the system cannot thrive even in absence of predation. Local stability of the system is obtained in absence of one or more of the predators and in presence of all the predators. Moreover, it is shown that the system undergoes Hopf bifurcation when the carrying capacity of macro-algae crosses certain critical value. Computer simulations have been carried out to illustrate various analytical results.

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Section: Introductionmentioning

confidence: 62%

Section: Introductionmentioning

confidence: 99%

Stage-Structured Cannibalism in a Ratio-Dependent System with Constant Prey Refuge and Harvesting of Matured Predator

Bhattacharyya

Pal

2016

Differ Equ Dyn Syst

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“…Here, we report the simulations to investigate the behavior of systems (2.1) and (3.1), performed using MatLab. The set of parameter values are chosen within the range prescribed in various previous literature sources 24,27,28,33,34 , and are given in Table 1. Values of parameters are arbitrary and have been used for illustration purpose only.…”

Section: Numerical Simulationmentioning

confidence: 99%

Effect of Time Delay in a Cannibalistic Stage-Structured Predator–prey Model With Harvesting of an Adult Predator: The Case of Lionfish

Maji¹,

Tiwari

Samanta

et al. 2019

J. Biol. Syst.

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The progressive and increasing invasion of an opportunistic predator, the lionfish (Pterois volitans) has become a major threat for the delicate coral-reef ecosystem. The herbivore fish populations, in particular of Parrotfish, are taking the consequences of the lionfish invasion and then their control function on macro-algae growth is threatened. In this paper, we developed and analyzed a stage-structured mathematical model including P. volitans (lionfish), a cannibalistic predator, and a Parrotfish, its potential prey. As control upon the over predation, a rational harvest term has been considered. Further, to make the system more realistic, a delay in the growth rate of juvenile P. volitans population has been incorporated. We performed a global sensitivity analysis to identify important parameters of the system having significant correlations with the fishes. We observed that the system generates transcritical bifurcation, which takes the P. volitans-free equilibrium to the coexistence equilibrium on increasing the values of predation rate of adult P. volitans on Parrotfish. Further increase in the values of the predation rate of adult P. volitans on Parrotfish drives the system into Hopf bifurcation, which induces oscillation around the coexistence equilibrium. Moreover, the conversion efficiency due to cannibalism also has the property to alter the stability behavior of the system through Hopf bifurcation. The effect of time delay on the dynamics of the system is extensively studied and it is observed that the system develops chaotic dynamics through period-doubling oscillations for large values of time delay. However, if the system is already oscillatory, then the large values of time delay causes extinction of P. volitans from the system. To illustrate the occurrence of chaotic dynamics in the system, we drew the Poincaré map and also computed the Lyapunov exponents.

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“…Похожие работы, направленные на изучение возникающих динамических режимов, проводятся и на основе аппарата дифференциальных уравнений, например [29,30]. Нередко встречаются исследования, посвященные изучению динамики сообществ типа «хищник -жертва», когда жертва или хищник представлены несколькими видами [8,[31][32][33][34][35][36][37], или же когда одна из составляющих сообщества подвергается изъятию [38][39][40].В работах, посвященных изучению динамики системы «хищник -жертва» с учетом возрастной детализации или стадий развития, используются в основном модели с непрерывным временем [41][42][43][44][45][46][47][48][49][50][51][52][53], при этом системы с дискретным временем применяются реже [54][55][56]. В частности, можно выделить работы, в которых рассматривается влияние возрастной структуры либо хищника [42,55], либо жертвы на развитие сообщества [56][57][58].…”

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“…В работах, посвященных изучению динамики системы «хищник -жертва» с учетом возрастной детализации или стадий развития, используются в основном модели с непрерывным временем [41][42][43][44][45][46][47][48][49][50][51][52][53], при этом системы с дискретным временем применяются реже [54][55][56]. В частности, можно выделить работы, в которых рассматривается влияние возрастной структуры либо хищника [42,55], либо жертвы на развитие сообщества [56][57][58].…”

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Modeling the Dynamics of Predator-Prey Community with Age Structures

Неверова¹,

Zhdanova²,

Frisman³

2019

Math.Biol.Bioinf.

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A model of the predator-prey community has been proposed with specific stages of individual development and the seasonality of breeding processes. It is assumed each of the species has an age structure with two stages of development. The case typical for the community “Arctic fox – rodents” is modeled. An analytical and numerical study of the model proposed is made. It is shown that periodic, quasi-periodic and chaotic oscillations can occur in the system, as well as a shift in the dynamics mode as a result of changes in the current sizes of the community’s populations. The model proposed demonstrates long-period oscillations with time delay like auto-oscillations in the classical model of Lotka-Volterra. It is shown that a transition from stable dynamics to quasi-periodic oscillations and vise verse is possible in the system, while an increase in the values of the half capturing saturation coefficient reduces the possibility of quasiperiodic oscillation emergence. Simulations demonstrate the growth in predator’s consumption of the prey average number expands the zones of multistability and quasi-periodic dynamics in the stability area of nontrivial fixed point. Therefore, the variation of the current population size of the community can lead to a change in the dynamic mode observed. The scenarios of transition from stationary dynamics to community’s population fluctuations are analyzed with different values of population parameters determining the dynamics of both species and their interaction coefficient. The model shows both sustainable community development and various complex fluctuations of interacting species. At the same time, the prey dynamics affects the predator one: the prey population fluctuations initiate predator oscillations like prey’s fluctuations, while the intrapopulation parameters of the predator can give to both stationary and fluctuating dynamic modes.

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The role of space in stage-structured cannibalism with harvesting of an adult predator

Cited by 11 publications

References 25 publications

Stage-Structured Cannibalism in a Ratio-Dependent System with Constant Prey Refuge and Harvesting of Matured Predator

Stage-Structured Cannibalism in a Ratio-Dependent System with Constant Prey Refuge and Harvesting of Matured Predator

Effect of Time Delay in a Cannibalistic Stage-Structured Predator–prey Model With Harvesting of an Adult Predator: The Case of Lionfish

Modeling the Dynamics of Predator-Prey Community with Age Structures

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