Stability and Hopf Bifurcation in a delayed ratio dependent Holling–Tanner type model

Çelik, Canan

doi:10.1016/j.amc.2014.11.086

Cited by 15 publications

(22 citation statements)

References 41 publications

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“…Furthermore, we will will extend work in [47] by incorporating maturation delay for prey and gestation delay for predator into system (4) in this paper. Due to population crowding, prey population dynamics is delayed by maturation delay τ 1 ≥ 0 [44]; negative feedback delay τ 2 ≥ 0 is assumed in gestation delay for predator population growth [29].…”

Section: ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ẋ (T) = X(t − τ )(1 − X(t − τ )) − X(t − τ )Y(t)mentioning

confidence: 99%

“…Recently, many theoreticians and experimentalists have discussed dynamical behavior of prey-predator system with Holling-Tanner functional response, it reveals that time delay may cause the loss of stability and other complicated dynamical behavior such as the periodic structure and bifurcation phenomenon [29,31,32,35,41,44,47]. By considering time delay for both prey and predator population, system (3) is extended in [47], which is as follows:…”

Section: ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ẋ (T) = X(t )(1 − X(t )) − X(t )Y(t) X(t ) + αYmentioning

confidence: 99%

“…In this paper, we will extend work in [47] by incorporating commercial harvesting on predator into system (4). It is assumed that z(t) represents commercial harvest effort amount on predator population.…”

Section: ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ẋ (T) = X(t − τ )(1 − X(t − τ )) − X(t − τ )Y(t)mentioning

confidence: 99%

“…The algebraic equation in system (9) contains no differentiated variables, hence leading matrix A(t) has a corresponding zero row. [47] is composed of delayed differential equations, only discuss interaction and coexistence mechanism of prey and predator population. Compared with system proposed in [47], an algebraic equation is incorporated into system (7), which focuses on economic interest of commercial harvest effort on predator.…”

Section: ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ẋ (T) = X(t − τ )(1 − X(t − τ )) − X(t − τ )Y(t)mentioning

confidence: 99%

“…[47] is composed of delayed differential equations, only discuss interaction and coexistence mechanism of prey and predator population. Compared with system proposed in [47], an algebraic equation is incorporated into system (7), which focuses on economic interest of commercial harvest effort on predator. Hence, system (7) not only investigates interaction and coexistence mechanism of population, but also studies dynamical behavior due to variation of economic interest.…”

Section: ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ẋ (T) = X(t − τ )(1 − X(t − τ )) − X(t − τ )Y(t)mentioning

confidence: 99%

See 4 more Smart Citations

Modeling and analysis in a prey–predator system with commercial harvesting and double time delays

Liu¹,

Lü²,

Zhang³

et al. 2016

Applied Mathematics and Computation

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Section: ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ẋ (T) = X(t − τ )(1 − X(t − τ )) − X(t − τ )Y(t)mentioning

confidence: 99%

Section: ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ẋ (T) = X(t )(1 − X(t )) − X(t )Y(t) X(t ) + αYmentioning

confidence: 99%

Section: ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ẋ (T) = X(t − τ )(1 − X(t − τ )) − X(t − τ )Y(t)mentioning

confidence: 99%

Section: ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ẋ (T) = X(t − τ )(1 − X(t − τ )) − X(t − τ )Y(t)mentioning

confidence: 99%

Section: ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ẋ (T) = X(t − τ )(1 − X(t − τ )) − X(t − τ )Y(t)mentioning

confidence: 99%

See 3 more Smart Citations

Modeling and analysis in a prey–predator system with commercial harvesting and double time delays

Liu¹,

Lü²,

Zhang³

et al. 2016

Applied Mathematics and Computation

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Global stability of a periodic Holling‐Tanner predator‐prey model

Lisena

2018

Math Methods in App Sciences

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MSC Classification: 34D23; 34C25; 92D25This paper is concerned with the global dynamics of a Holling-Tanner predator-prey model with periodic coefficients. We establish sufficient conditions for the existence of a positive solution and its global asymptotic stability.The stability conditions are first given in average form and afterward as pointwise estimates. In the autonomous case, the previous criteria lead to a known result.

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