Global analysis of a delayed density dependent predator–prey model with Crowley–Martin functional response

Tripathi, Jai Prakash; Tyagi, Swati; Abbas, Syed

doi:10.1016/j.cnsns.2015.06.008

Cited by 112 publications

(35 citation statements)

References 48 publications

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“…Zhou [47] presented qualitative analysis of the predator-prey model for Crowley-Martin functional responses. Tripathi et al [48] applied Crowley-Martin functional response on a delayed density dependent predator-prey model. Li et al [49] presented a predator-prey model with Crowley-Martin functional response for positive periodic solutions.…”

Section: Introductionmentioning

confidence: 99%

Bifurcation and Chaos of a Discrete Predator-Prey Model with Crowley–Martin Functional Response Incorporating Proportional Prey Refuge

Santra

Mahapatra²,

Phaijoo

2020

Mathematical Problems in Engineering

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The paper investigates the dynamical behaviors of a two-species discrete predator-prey system with Crowley–Martin functional response incorporating prey refuge proportional to prey density. The existence of equilibrium points, stability of three fixed points, period-doubling bifurcation, Neimark–Sacker bifurcation, Marottos chaos, and Control Chaos are analyzed for the discrete-time domain. The time graphs, phase portraits, and bifurcation diagrams are obtained for different parameters of the model. Numerical simulations and graphics show that the discrete model exhibits rich dynamics, which also present that the system is a chaotic and complex one. This paper attempts to present a feedback control method which can stabilize chaotic orbits at an unstable equilibrium point.

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Section: Introductionmentioning

confidence: 99%

Bifurcation and Chaos of a Discrete Predator-Prey Model with Crowley–Martin Functional Response Incorporating Proportional Prey Refuge

Santra

Mahapatra²,

Phaijoo

2020

Mathematical Problems in Engineering

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“…Cao and Jiang [10] studied a reaction-diffusion type predator-prey model with Crowley-Martin functional response, mainly focusing on Turing-Hopf bifurcation. In [11], the authors studied a predator-prey model with delay and Crowley-Martin functional response, mainly considering the stability and Hopf bifurcation. In [12], the authors considered a predator-prey model with Crowley-Martin functional response, mainly studying the flip bifurcation and Neimark-Sacker bifurcation.…”

Section: Introductionmentioning

confidence: 99%

Turing instability and Hopf bifurcation in a predator–prey model with delay and predator harvesting

et al. 2019

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In this paper, we study a predator-prey model with delay and harvesting on predator. We give the conditions for stability and Turing instability of coexisting equilibrium by analyzing the eigenvalue spectrum. By using delay as a bifurcation parameter we give conditions for occurrence of Hopf bifurcation. We investigate the property of bifurcating period solutions by calculating the normal form. We perform some numerical simulations to support our theoretical result. Our results show that diffusion and delay are two factors that should be considered in establishing the predator-prey model, since they can induced the Turing instability and spatially bifurcating period solutions.

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“…Predator-prey models with Holling types I, II, III, and IV responses were investigated in [9][10][11][12]. The Beddington-DeAngelis, Crowley-Martin, and ratio-dependent functional responses were also further considered in [13][14][15]. But limited work is available on predator-prey model with mutualism.…”

Section: Introductionmentioning

confidence: 99%

“…Furthermore, it is more realistic and reasonable that the future state of population dynamics is determined by not only the present states but also the past [17,18]. Up to now, there have been many works considering the effect of time delay [13,14,19,20]. Then, taking time delay on mutualistic interaction and predation into account, model (2) can be modified as the following model:…”

Section: Introductionmentioning

confidence: 99%

Dynamical Behavior of a Stochastic Delayed One-Predator and Two-Mutualistic-Prey Model with Markovian Switching and Different Functional Responses

Zhang

Hong

2016

Discrete Dynamics in Nature and Society

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We propose a stochastic delayed one-predator and two-mutualistic-prey model perturbed by white noise and telegraph noise. By theM-matrix analysis and Lyapunov functions, sufficient conditions of stochastic permanence and extinction are established, respectively. These conditions are all dependent on the subsystems’ parameters and the stationary probability distribution of the Markov chain. We also investigate another asymptotic property and finally give two examples and numerical simulations to illustrate main results.

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Global analysis of a delayed density dependent predator–prey model with Crowley–Martin functional response

Cited by 112 publications

References 48 publications

Bifurcation and Chaos of a Discrete Predator-Prey Model with Crowley–Martin Functional Response Incorporating Proportional Prey Refuge

Bifurcation and Chaos of a Discrete Predator-Prey Model with Crowley–Martin Functional Response Incorporating Proportional Prey Refuge

Turing instability and Hopf bifurcation in a predator–prey model with delay and predator harvesting

Dynamical Behavior of a Stochastic Delayed One-Predator and Two-Mutualistic-Prey Model with Markovian Switching and Different Functional Responses

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