A delayed prey–predator model with Crowley–Martin‐type functional response including prey refuge

Maiti, Alakes; Dubey, B.; Tushar, Jai

doi:10.1002/mma.4429

Cited by 28 publications

(9 citation statements)

References 39 publications

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“…To describe the interaction of plankton more realistic, biological intrinsic disciplines and external relationships, such as additional food, prey refuge, and stage structure, have been taken into consideration in the formulation of plankton model. As an important intrinsic factor of biology, the body size of organism reflects its adaptive modification in response to the prevailing abiotic and biotic environment .…”

Section: Introductionmentioning

confidence: 99%

Stationary distribution and extinction of a stochastic nutrient‐phytoplankton‐zooplankton model with cell size

2020

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In this paper, we study a stochastic nutrient‐phytoplankton‐zooplankton model with cell size that represents the interaction between internal mechanism of species and external environment. We first investigate the existence and uniqueness of the global positive solution with positive initial values. Then we construct sufficient conditions for the existence of an ergodic stationary distribution of positive solution. Once more, we find that large noise intensities cause the extinctions of phytoplankton and zooplankton. Finally, numerical simulations are given to verify the correctness of theoretical results.

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Section: Introductionmentioning

confidence: 99%

Stationary distribution and extinction of a stochastic nutrient‐phytoplankton‐zooplankton model with cell size

2020

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“…[7][8][9][10] The delay due to maturation time of prey, gestation time of predator, and hunting can induce periodic solutions as well as chaos in prey-predator model. [11][12][13][14][15] Hence, the exploration of prey-predator model with several natural factors is getting more popularity because of interesting biological phenomenon.…”

Section: Introductionmentioning

confidence: 99%

Complex dynamics of a discrete fractional‐order Leslie‐Gower predator‐prey model

Singh

Elsadany

Elsonbaty

2019

Math Methods in App Sciences

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A proposed discretized form of fractional‐order prey‐predator model is investigated. A sufficient condition for the solution of the discrete system to exist and to be unique is determined. Jury stability test is applied for studying stability of equilibrium points of the discretized system. Then, the effects of varying fractional order and other parameters of the systems on its dynamics are examined. The system undergoes Neimark‐Sacker and flip bifurcation under certain conditions. We observe that the model exhibits chaotic dynamics following stable states as the memory parameter α decreases and step size h increases. Theoretical results illustrate the rich dynamics and complexity of the model. Numerical simulation validates theoretical results and demonstrates the presence of rich dynamical behaviors include S‐asymptotically bounded periodic orbits, quasi‐periodicity, and chaos. The system exhibits a wide range of dynamical behaviors for fractional‐order α key parameter.

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“…Holling considered it nonlinear function of prey species that saturates at a level. Further, it was considered a function of prey and predator both by several authors [6,10,13,14].…”

Section: Introductionmentioning

confidence: 99%

Stability and Bifurcation of a Prey-Predator System with Additional Food and Two Discrete Delays

Kumar¹,

Dubey²

2021

Computer Modeling in Engineering &Amp; Sciences

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In this paper, the impact of additional food and two discrete delays on the dynamics of a prey-predator model is investigated. The interaction between prey and predator is considered as Holling Type-II functional response. The additional food is provided to the predator to reduce its dependency on the prey. One delay is the gestation delay in predator while the other delay is the delay in supplying the additional food to predators. The positivity, boundedness and persistence of the solutions of the system are studied to show the system as biologically well-behaved. The existence of steady states, their local and global asymptotic behavior for the non-delayed system are investigated. It is shown that (i) predator's dependency factor on additional food induces a periodic solution in the system, and (ii) the two delays considered in the system are capable to change the status of the stability behavior of the system. The existence of periodic solutions via Hopf-bifurcation is shown with respect to both the delays. Our analysis shows that both delay parameters play an important role in governing the dynamics of the system. The direction and stability of Hopf-bifurcation are also investigated through the normal form theory and the center manifold theorem. Numerical experiments are also conducted to validate the theoretical results.

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A delayed prey–predator model with Crowley–Martin‐type functional response including prey refuge

Cited by 28 publications

References 39 publications

Stationary distribution and extinction of a stochastic nutrient‐phytoplankton‐zooplankton model with cell size

Stationary distribution and extinction of a stochastic nutrient‐phytoplankton‐zooplankton model with cell size

Complex dynamics of a discrete fractional‐order Leslie‐Gower predator‐prey model

Stability and Bifurcation of a Prey-Predator System with Additional Food and Two Discrete Delays

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