A bifurcation path to chaos in a time-delay fisheries predator–prey model with prey consumption by immature and mature predators

Boonrangsiman, S.; Bunwong, Kornkanok; Moore, Elvin J.

doi:10.1016/j.matcom.2015.12.009

Cited by 16 publications

(10 citation statements)

References 32 publications

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“…Ref. [12,13] also have paid great attention to discussing the effect with stage structure in predator-prey models. In [14], Wang et al considered a delayed ratio-dependent predator-prey system with Holling type III functional response and stage structure for the predator:…”

Section: Introductionmentioning

confidence: 99%

Hopf bifurcation analysis in a predator–prey model with two time delays and stage structure for the prey

Peng

Zhang

2018

Adv Differ Equ

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In this paper, a stage-structured predator-prey model with Holling type III functional response and two time delays is investigated. By analyzing the associated characteristic equation, its local stability and the existence of Hopf bifurcation with respect to both delays are studied. Based on the normal form method and center manifold theorem, the explicit formulas are derived to determine the direction of Hopf bifurcation and the stability of bifurcating period solutions. Finally, the effectiveness of theoretical analysis is verified via numerical simulations. This study may be helpful in understanding the behavior of ecological environment.

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Section: Introductionmentioning

confidence: 99%

Hopf bifurcation analysis in a predator–prey model with two time delays and stage structure for the prey

Peng

Zhang

2018

Adv Differ Equ

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“…assuming that the wave of fish movement is traveling at a constant speed v. Letting x(z) = X(r, t), and y(z) = Y (r, t), Eq. (3) becomes vx = wx + cvy (4) and (2) becomes…”

Section: Traveling Wave Coordinatementioning

confidence: 99%

“…Limited data can be found that give time series of the fish population but the measurements were done for very long time intervals, in years not in days or weeks that could be used to calibrate our model. The studies cited in the introduction section [1][2][3][4][5][6][7][8][9][10][11] constructed their models based on general observations and not on any rigorous physical data measurements and relatively crude data was used in their model simulations. In fact, for this reason, our modeling should be a valuable springboard and provide an impetus for researchers to collect physical data that are more relevant to the effort at fisheries management.…”

Section: Stability Analysesmentioning

confidence: 99%

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Stability analysis and traveling wave solution of a reaction–diffusion model for fish population incorporating time-dependent recruitment intensity

Suksamran

Lenbury

2019

Adv Differ Equ

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From the standpoint of fishery management, an essential component of the basic information upon which policy can be based consists of intelligence from field data and computations. In certain situations, these studies can provide quite a great deal of the necessary information. However, in other situations they have not been able to give unequivocal answers to important questions, especially where several influential factors are involved in the whole jigsaw of the complex fishery system, in which their relative abundance may vary with the intensity of the recruitment effort or with spatial migration. Here, we propose and analyze a reaction-diffusion model for the fish population incorporating time-dependent fishery intensity. Using the traveling wave coordinate, we derive analytical solutions to the model system. Conditions on the system parameters are derived which ensure stability of the system under study. Phase portrait and traveling wave solution are plotted and discussed in order to gain better insights into the spatial movement of the fish population in time.

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“…Their model is fully spatialized and oceanographic and biological data were utilized to parameterize movements which naturally react to environmental variations. More recently, Boonrangsiman et al [14] proposed a stage-structure model of fisheries which incorporated a time delay. The single prey population and a predator population were differentiated with respect to their reproduction ability into an immature and a mature stage.…”

Section: Introductionmentioning

confidence: 99%

Analysis of advection-diffusion-reaction model for fish population movement with impulsive tagging: stability and traveling wave solution

2019

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So far, mobility in fish population has not been given sufficient attention, although movement and spatial heterogeneity can be an important dynamic feature that plays a critical role in their exploitation. Having a qualitative framework to describe and estimate movement and growth based on tagging data is necessary for efficient control and management of the fishing industry. Here, we construct an advection-diffusion-reaction model for the fish population structured to track the population densities of both the tagged fish and the tag-free fish, in which the impulsive tagging practice is incorporated, while continuous tagging is assumed to be done on off springs of trackable tagged fish, or on those in the same swarm as the trackable tagged fish. Using the traveling wave coordinate, we derive analytical expression for the solutions to the model system. We derive the explicit expression for the level of tagged fish which increases in a periodic impulsive fashion. Stability and phase plane analyses are also carried out to determine different behavior permitted by the model system.

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A bifurcation path to chaos in a time-delay fisheries predator–prey model with prey consumption by immature and mature predators

Cited by 16 publications

References 32 publications

Hopf bifurcation analysis in a predator–prey model with two time delays and stage structure for the prey

Hopf bifurcation analysis in a predator–prey model with two time delays and stage structure for the prey

Stability analysis and traveling wave solution of a reaction–diffusion model for fish population incorporating time-dependent recruitment intensity

Analysis of advection-diffusion-reaction model for fish population movement with impulsive tagging: stability and traveling wave solution

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