Dynamics of an additional food provided predator–prey system with prey refuge dependent on both species and constant harvest in predator

Mondal, Sudeshna; Samanta, G. P.

doi:10.1016/j.physa.2019.122301

Cited by 59 publications

(24 citation statements)

References 28 publications

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“…Like acute fear of prey to predators, it can move prey to move places or ecosystems in the long term and return when the ecosystem is considered safe by prey. Like the behavior of birds that are afraid of the sound of predators, with the physiological state of fear in birds, they fly away or migrate since the first danger appears [9] [10]. Such events can reduce the reproduction rate of birds in the long term, although in the short term it is beneficial because it saves adult prey species.…”

Section: Introductionmentioning

confidence: 99%

Impact of Fear Behavior on Prey Population Growth Prey-Predator Interaction

Pratama

2022

BAREKENG: J. Il. Mat. & Ter.

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Experiments on the living environment of vertebrate ecosystems, it has been shown that predators have a massive influence on the demographic growth rate of prey. The proposed fear effect is a mathematical model that affects the reproductive growth rate of prey with the Holling Type I interaction model. Mathematical analysis of the prey-predator model shows that a strong anti-predator response can provide stability for prey-predator interactions. The parameter area taken will be shown for the extinction of the prey population, the balance of population survival, and the balance between the prey birth rate and the predator death rate. Numerical simulations were given to investigate the biological parameters of the population (birth rate, natural mortality of prey, and predators). Another numerical illustration that is seen is the behavior of prey which is less sensitive in considering the risk of predators with the growth rate of prey.

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Section: Introductionmentioning

confidence: 99%

Impact of Fear Behavior on Prey Population Growth Prey-Predator Interaction

Pratama

2022

BAREKENG: J. Il. Mat. & Ter.

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“…Researchers have mainly used the dynamic nature of predator-prey model with linear prey refuge (that is, mx amounts of prey are unavailable to the predator, where m ∈ (0, 1) is the coefficient of refuge and x is the biomass of prey species) with Volterra response [20][21][22]. Recently, Mondal and Samanta have studied the dynamics of the predator-prey system with prey refuge dependent on both species (that is, mxy amounts of prey are free from the predator risk, where 0 < 1 − my < 1, m is prey refuge coefficient, x is the biomass of prey population, and y is the biomass of predator population) in the presence of additional food (for details, see [23]). In 2020, Mondal and Samanta [11] have also analyzed the dynamics of predatorprey interaction having nonlinear prey refuge function Φ(x, y) � (mxy/(a + y)) which is the amount of prey that are free from predation, where a is half saturation constant and y is the biomass of predator population.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of a Predator‐Prey Population in the Presence of Resource Subsidy under the Influence of Nonlinear Prey Refuge and Fear Effect

2021

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In this work, our aim is to investigate the impact of a non-Kolmogorov predator-prey-subsidy model incorporating nonlinear prey refuge and the effect of fear with Holling type II functional response. The model arises from the study of a biological system involving arctic foxes (predator), lemmings (prey), and seal carcasses (subsidy). The positivity and asymptotically uniform boundedness of the solutions of the system have been derived. Analytically, we have studied the criteria for the feasibility and stability of different equilibrium points. In addition, we have derived sufficient conditions for the existence of local bifurcations of codimension 1 (transcritical and Hopf bifurcation). It is also observed that there is some time lag between the time of perceiving predator signals through vocal cues and the reduction of prey’s birth rate. So, we have analyzed the dynamical behaviour of the delayed predator-prey-subsidy model. Numerical computations have been performed using MATLAB to validate all the analytical findings. Numerically, it has been observed that the predator, prey, and subsidy can always exist at a nonzero subsidy input rate. But, at a high subsidy input rate, the prey population cannot persist and the predator population has a huge growth due to the availability of food sources.

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“…Hence, one may argue that it is almost mandatory at some stage to include harvest in modelling such species. Excellent studies which address the role of harvest may be obtained in [31][32][33][34][35][36][37][38][39][40]. Now, following [41], there are in principle four factors which may explain oscillatory behaviour in (fish) populations.…”

Section: Introductionmentioning

confidence: 99%

Compensatory and overcompensatory dynamics in prey–predator systems exposed to harvest

Wikan¹,

Kristensen²

2021

J. Appl. Math. Comput.

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Density dependent prey–predator systems under the impact of harvest are considered. The recruitment functions for both the prey and predator belong to the Deriso–Schnute family which allow us to study how the dynamical behaviour of both populations changes when compensatory density dependence turns overcompensatory. Depending on the degree of overcompensation, we show in the case of no harvest that an increase of the fecundity of the prey always acts in a destabilizing fashion. If the degree of overcompensation becomes sufficiently large, such an increase can lead to large amplitude chaotic oscillations of the prey, which actually may drive the predator population to extinction. The impact of harvest also depends on the degree of overcompensatory density dependence. If only the prey is the target population, increased harvest in general seems to stabilize the dynamics. On the other hand, harvesting only the predator may in some cases tend to stabilize dynamics, but there are also parameter regions where this turns out to be a strong destabilizing effect.

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Dynamics of an additional food provided predator–prey system with prey refuge dependent on both species and constant harvest in predator

Cited by 59 publications

References 28 publications

Impact of Fear Behavior on Prey Population Growth Prey-Predator Interaction

Impact of Fear Behavior on Prey Population Growth Prey-Predator Interaction

Dynamics of a Predator‐Prey Population in the Presence of Resource Subsidy under the Influence of Nonlinear Prey Refuge and Fear Effect

Compensatory and overcompensatory dynamics in prey–predator systems exposed to harvest

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