Dynamics and pattern formations in a three-species predator-prey model with two prey-taxis

Wang, Jinfeng; Guo, Xinxin

doi:10.1016/j.jmaa.2019.02.071

Cited by 15 publications

(4 citation statements)

References 25 publications

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“…In [11], authors have investigated the existence, uniqueness, and long-term behavior of the global solution for a class of predator-prey system with Beddington-DeAngelis functional response and nonlinear prey-taxis under free boundary. For more details about the importance of taxis on the population dynamics, we refer the readers to [9,[28][29][30] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

A predator–prey system with prey social behavior and generalized Holling III functional response: Role of predator‐taxis on spatial patterns

Souna

Tiwari

Belabbas

et al. 2023

Math Methods in App Sciences

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In this paper, we investigate the intrinsic impact of the predator‐taxis coefficient on the formation of spatial patterns in a predator–prey system with prey social behavior subject to Neumann boundary conditions. By treating the predator‐taxis coefficient as a potential critical parameter for Turing bifurcation, we observe that the Turing pattern is fully captured by three distinct critical thresholds. Meanwhile, utilizing weakly nonlinear analysis and the amplitude equation, we establish the direction of Turing bifurcation. Our mathematical analysis reveals that the inclusion of the predator‐taxis coefficient in the predator–prey system may lead to the emergence of either subcritical or supercritical Turing bifurcation. Our numerical experiments confirm the theoretical findings and exhibit various spatial patterns with different values of predator‐taxis coefficients.

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Section: Introductionmentioning

confidence: 99%

A predator–prey system with prey social behavior and generalized Holling III functional response: Role of predator‐taxis on spatial patterns

Souna

Tiwari

Belabbas

et al. 2023

Math Methods in App Sciences

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“…Wang discussed the effects of prey-taxis on the existence and stability of nonconstant steady states, gave the bifurcation type and stability of the bifurcation curve, and provided a stable wave model selection mechanism for the reaction-diffusion system with prey-taxis in the 1D case in [10]; Wang found that the homogeneous positive steady states lose stability as χ increases, and got the existence of non-homogeneous positive steady states and the stability of bifurcating solutions for the higher-dimensional case in [11]. Moreover, the prey can also adjust the corresponding position to reduce the risk of being caught, which is called predator-taxis [12]. And for the systems with three species [13,14], the authors investigated the global existence of the system solutions and the local stability conditions of the equilibria.…”

Section: Introductionmentioning

confidence: 99%

Steady states of a diffusive predator-prey model with prey-taxis and fear effect

Cao¹,

Li²,

Hao

2022

Preprint

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In this paper, a diffusive predator-prey system with prey-taxis response subject to Neumann boundary conditions is considered. First, the stability of the positive equilibrium and the conditions for the occurrence of Hopf bifurcation are provided. Second, the existence of nonconstant steady states is proved by applying the the bifurcation theory of Crandall and Rabinowitz, bifurcation types and stability of the bifurcation solutions are analyzed. Finally, numerical simulation results are carried out to verify the theoretical results.

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“…Moreover, the prey can also adjust the corresponding position to reduce the risk of being caught, which is called predator-taxis [21]. Also, for the systems with three species [22][23][24], the authors investigated the global existence of the system solutions and the local stability conditions of the equilibria. More details about chemotaxis can be seen in [25][26][27][28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

Steady states of a diffusive predator-prey model with prey-taxis and fear effect

Cao

Hao

2022

Bound Value Probl

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In this paper, a diffusive predator-prey system with a prey-taxis response subject to Neumann boundary conditions is considered. The stability, the Hopf bifurcation, the existence of nonconstant steady states, and the stability of the bifurcation solutions of the system are analyzed. It is proved that a high level of prey-taxis can stabilize the system, the stability of the positive equilibrium is changed when χ crosses $\chi _{0}$ χ 0 , and the Hopf bifurcation occurs for the small s. The system admits nonconstant positive solutions around $(\bar{u}, \bar{v}, \chi _{i} )$ ( u ¯ , v ¯ , χ i ) , the stability of bifurcating solutions are controlled by $\int _{\Omega} \Phi _{i}^{3} \,\mathrm{d}x$ ∫ Ω Φ i 3 d x and $\int _{\Omega} \Phi _{i}^{4} \,\mathrm{d}x$ ∫ Ω Φ i 4 d x . Finally, numerical simulation results are carried out to verify the theoretical findings.

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Dynamics and pattern formations in a three-species predator-prey model with two prey-taxis

Cited by 15 publications

References 25 publications

A predator–prey system with prey social behavior and generalized Holling III functional response: Role of predator‐taxis on spatial patterns

A predator–prey system with prey social behavior and generalized Holling III functional response: Role of predator‐taxis on spatial patterns

Steady states of a diffusive predator-prey model with prey-taxis and fear effect

Steady states of a diffusive predator-prey model with prey-taxis and fear effect

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