Role of time delay and harvesting in some predator–prey communities with different functional responses and intra-species competition

Barman, Binandita; Ghosh, Bapan

doi:10.1080/02286203.2021.1983747

Cited by 15 publications

(10 citation statements)

References 47 publications

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“…The upper portion of the Hopf bifurcation curve represents a stable region, whereas the lower portion of the curve represents an unstable region. In general, the increase in the growth rate of the prey α destabilised the system, whereas the increase in the mortality rate of the predator β stabilised it, and this is in agreement with what was mentioned in [49]. The Hopf bifurcation points can only occur for α ≥ 1.21 and 1.29 for the one-term and two-term methods, respectively.…”

Section: Hopf Bifurcation Maps and Limit Cyclesupporting

confidence: 88%

“…The present study demonstrated the high accuracy and utility of the semi-analytical model for studying the dynamics of specific biological systems, such as delayed diffusive multispecies Lotka-Volterra food chains or two-prey/one-predator systems [22]. Furthermore, in the light of harvesting in non-diffusive models [47,49], one more interesting investigation would be to vary the mortality rate as a control parameter, and examine the impacts of harvesting upon the diffusive system (1) and (2).…”

Section: Discussionmentioning

confidence: 63%

“…The standard literature on bifurcation theory and dynamical systems [43][44][45][46] has clarified the Hopf bifurcation theory. Moreover, many researchers discussed the techniques to find the Jacobian matrix, the conditions for stability, and stability switching for prey-predator models [47][48][49][50][51]. The stability of the semi-analytical model was studied here, and the findings were used to investigate the effects of the three time delays of the species on the stability of the system (1) and ( 2).…”

Section: Hopf Bifurcations and Stability Analysis 41 Theoretical Fram...mentioning

confidence: 99%

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Stability Analysis of a Diffusive Three-Species Ecological System with Time Delays

Noufaey¹,

Khaled²

2021

Symmetry

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In this study, the dynamics of a diffusive Lotka–Volterra three-species system with delays were explored. By employing the Galerkin Method, which generates semi-analytical solutions, a partial differential equation system was approximated through mathematical modeling with delay differential equations. Steady-state curves and Hopf bifurcation maps were created and discussed in detail. The effects of the growth rate of prey and the mortality rate of the predator and top predator on the system’s stability were demonstrated. Increase in the growth rate of prey destabilised the system, whilst increase in the mortality rate of predator and top predator stabilised it. The increase in the growth rate of prey likely allowed the occurrence of chaotic solutions in the system. Additionally, the effects of hunting and maturation delays of the species were examined. Small delay responses stabilised the system, whilst great delays destabilised it. Moreover, the effects of the diffusion coefficients of the species were investigated. Alteration of the diffusion coefficients rendered the system permanent or extinct.

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Section: Hopf Bifurcation Maps and Limit Cyclesupporting

confidence: 88%

Section: Discussionmentioning

confidence: 63%

Section: Hopf Bifurcations and Stability Analysis 41 Theoretical Fram...mentioning

confidence: 99%

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Stability Analysis of a Diffusive Three-Species Ecological System with Time Delays

Noufaey¹,

Khaled²

2021

Symmetry

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“…In other words, the timescale of the optimization was assumed to be much shorter, than the timescale of the dynamics itself. On the other hand, the effect of delay of action of resources with respect to preys has been discussed in [13,14]. There, the delay time was a fixed parameter.…”

Section: Introductionmentioning

confidence: 99%

Instability of oscillations in the Rosenzweig-MacArthur model of one consumer and two resources

Gawroński,

Borzì,

Kułakowski

2022

Preprint

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The system of two resources R1, R2 and one consumer C is investigated within the Rosenzweig-MacArthur model with Holling type II functional response. The rates βi of consumption of resources i = 1, 2 are coupled by the condition β1 + β2 = 1. The dynamic switching is introduced by a maximization of C: dβ1/dt = (1/τ )dC/dβ1, where the characteristic time τ is large but finite. The space of parameters where both resources coexist is explored numerically. The results indicate that oscillations of C and mutually synchronized Ri which appear at βi = 0.5 are destabilized for βi larger or smaller. Then, the system is driven to one of fixed points where either β1 > 0.5 and R1 < R2 or the opposite. This behaviour is explained as an inability of the consumer to change the preferred resource, once it is chosen.

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“…impacted the dynamic behavior of predator and prey in nature. It has been established that the stability of predator-prey models is effected by Allee effect, 1,2 predator interferance, 3 foraging facilitation, 4 population harvesting, 5 fear effect, 6 presence of intra-specific competition, 7 time delays, [8][9][10] etc.…”

mentioning

confidence: 99%

Multiple dynamics in a delayed predator‐prey model with asymmetric functional and numerical responses

Ghosh

Barman

Saha

2022

Math Methods in App Sciences

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We consider a predator‐prey model with dissimilar functional and numerical responses that induce an Allee effect. There is a time lag between consumption and digestion of prey biomass by predator. Hence, a time delay has been incorporated in the numerical response function. The system consists of two interior equilibria. Taking time delay as the bifurcation parameter, four different dynamic behaviors appear, viz., (R1) system undergoes no change in its stability for all time delay, (R2) system undergoes stability change, (R3) system undergoes stability switching, and (R4) system undergoes instability switching. Here, finding four distinct dynamics in a single population model with only one delay is a novelty in this contribution. This variation in dynamics emerges due to asymmetricity in functional and numerical responses. All the relevant theorems in establishing stability are provided, and these are verified numerically. We analytically prove that if an interior equilibrium is a saddle point in absence of time delay, then the equilibrium cannot be stabilized by varying the time delay. It is popularly believed that existence of two distinct pair of purely imaginary roots of the characteristic function leads to stability switching. However, we provide examples where the system remains unstable, stability changes, and instability switching occurs. This is another new and interesting observation in our work. The numerical examples are furnished with phase portraits, time series plots, bifurcation diagrams, and eigenvalues evaluation with delay, for better understanding. Our model with a single delay exhibits variety of dynamics, which were not explored before.

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Role of time delay and harvesting in some predator–prey communities with different functional responses and intra-species competition

Cited by 15 publications

References 47 publications

Stability Analysis of a Diffusive Three-Species Ecological System with Time Delays

Stability Analysis of a Diffusive Three-Species Ecological System with Time Delays

Instability of oscillations in the Rosenzweig-MacArthur model of one consumer and two resources

Multiple dynamics in a delayed predator‐prey model with asymmetric functional and numerical responses

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