Global bifurcation for a reaction–diffusion predator–prey model with Holling-II functional response and prey–taxis

Luo, Demou

doi:10.1016/j.chaos.2021.110975

Cited by 17 publications

(7 citation statements)

References 21 publications

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“…In this work, we apply the approach of test function to obtain a priori estimates of steady states that are different from the Moser iteration technique applied in [51]. By comparing with [52], we discover that the dynamics of system with Beddington–DeAngelis and Tanner functional responses is more complicated than the dynamics of model with Holling‐II functional response since we consider the interference among predators.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Global bifurcation for a Beddington–DeAngelis and Tanner predator–prey reaction–diffusion system with prey‐taxis

Luo,

Wang

2023

Math Methods in App Sciences

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The aim of this paper is to establish a precise illustration for the structure of the nonconstant steady states for a Beddington–DeAngelis and Tanner predator–prey reaction–diffusion system with prey‐taxis. We treat the nonlinear prey‐taxis as a bifurcation parameter to analyze the bifurcation structure of the system. Furthermore, the exported global bifurcation theorem, under a rather natural condition, offers the existence of nonconstant steady states. In the proof, a priori estimates of steady states will play an important role. The local stability analysis with a numerical simulation and bifurcation analysis are given. Finally, some conclusions including biological meanings are performed to summarize our main analytic results and future investigations.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Global bifurcation for a Beddington–DeAngelis and Tanner predator–prey reaction–diffusion system with prey‐taxis

Luo,

Wang

2023

Math Methods in App Sciences

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“…Proof Substituting ( 16)-( 19) into the second equation in (6) and collecting their h 3 -terms, 26) by i and integrating it over ,…”

Section: The Stability Of Bifurcation Solutionsmentioning

confidence: 99%

“…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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“…Additionally, in the absence of predators, the prey population is predicted to grow indefinitely, due to the same assumption. While the core tenets of the model are still widely applicable, several models have been proposed as improvements on the Lotka-Volterra model, including the Holling model [9,10], the Beddington-DeAngelis model [11], the ratio-dependent model [8,12], and so on. Over the years, various functional responses have been proposed and investigated by the research scientists.…”

Section: Introductionmentioning

confidence: 99%

“…In some cases, the species' movement might be directional [10,[18][19][20]. In fact, predators typically move toward areas with abundances of certain prey species so that they can easily find food.…”

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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Global bifurcation for a reaction–diffusion predator–prey model with Holling-II functional response and prey–taxis

Cited by 17 publications

References 21 publications

Global bifurcation for a Beddington–DeAngelis and Tanner predator–prey reaction–diffusion system with prey‐taxis

Global bifurcation for a Beddington–DeAngelis and Tanner predator–prey reaction–diffusion system with prey‐taxis

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

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

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