Pattern formation of a spatial predator–prey system

Sun, Gui‐Quan; Zhang, Juan; Song, Lipeng; Jin, Zhen; Li, Bai-Lian

doi:10.1016/j.amc.2012.04.071

Cited by 85 publications

(44 citation statements)

References 37 publications

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“…Previous work on (1.2) focuses on this equilibrium. For example, in [8,9], Turing patterns that bifurcate from A are observed in numerical simulations. In [10], conditions for Turing and Hopf bifurcations are derived, and the stability of the bifurcating periodic solutions is studied.…”

Section: Introductionmentioning

confidence: 99%

Travelling waves in the Holling–Tanner model with weak diffusion

2015

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For a wide range of parameters, we study travelling waves in a diffusive version of the Holling-Tanner predator-prey model from population dynamics. Fronts are constructed using geometric singular perturbation theory and the theory of rotated vector fields. We focus on the appearance of the fronts in various singular limits. In addition, periodic travelling waves of relaxation oscillation type are constructed using a recent generalization of the entryexit function.

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Section: Introductionmentioning

confidence: 99%

Travelling waves in the Holling–Tanner model with weak diffusion

2015

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“…Many researchers studied the dynamical behavior of the predator-prey system in ecology and contributed to growth of continuous models for large size populations [1][2][3][4][5][6][7][8][9][10][11][12][13]. Further, some authors have investigated the stability and spatial pattern formation of spatio-temporal models in predator-prey systems [14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Discrete-time dynamics of a system with crowding effect and predator partially dependent on prey

Dhar

Singh

Bhatti³

2015

Applied Mathematics and Computation

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“…Baek [2] investigated the pattern formations of a ratio-dependent predator-prey system with linear harvesting rate. Sun et al [26] studied the spatiotemporal complexity in a Holling-Tanner model and investigated how directed movement (migration) and random movement (diffusion) affect predator-prey dynamics. Rai et al [22] investigated the effects of random and directed animal movements of a 1D spatial nonlinear coupled reaction-diffusion system with a Holling type IV functional response.…”

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confidence: 99%

Complex dynamics of ecological systems under nonlinear harvesting: Hopf bifurcation and Turing instability

2014

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In this paper, we study the complex dynamics of a spatial nonlinear predator-prey system under harvesting. A modified Leslie-Gower model with Holling type IV functional response and nonlinear harvesting of prey is considered. We perform a detailed stability and Hopf bifurcation analysis of the spatial model system and determine the direction of Hopf bifurcation and stability of the bifurcating periodic solutions. Numerical simulations were performed to figure out how Turing patterns evolve under nonlinear harvesting. Simulation study leads to a few interesting sequences of pattern formation, which may be relevant in real world situations.

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Pattern formation of a spatial predator–prey system

Cited by 85 publications

References 37 publications

Travelling waves in the Holling–Tanner model with weak diffusion

Travelling waves in the Holling–Tanner model with weak diffusion

Discrete-time dynamics of a system with crowding effect and predator partially dependent on prey

Complex dynamics of ecological systems under nonlinear harvesting: Hopf bifurcation and Turing instability

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