Stability and cross-diffusion-driven instability in a diffusive predator–prey system with hunting cooperation functional response

Song, Danxia; Li, Chao; Song, Yongli

doi:10.1016/j.nonrwa.2020.103106

Cited by 42 publications

(23 citation statements)

References 44 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The lower limit of the stability of stripe structures is obtained by a linear stability analysis of (27) around ρ j = ρ S + δρ j (j = 1, 2, 3 respectively) for the steady state value ρ S . Substituting, from…”

Section: Weakly Nonlinear Analysismentioning

confidence: 99%

“…. The upper limit of the stability of hexagonal patterns is calculated by a linear stability analysis of (27) around 1, 2, 3). For the solution ρ H = ρ + H the eigenvalue λ 1 is always negative, while…”

Section: Weakly Nonlinear Analysismentioning

confidence: 99%

“…In particular, diffusion-driven instability, commonly known as Turing instability, leads to the occurrence of the so-called Turing patterns. The study of these patterns in spatial population models has recently seen an increasing activity and interest ( [14,15,23,[27][28][29][30]). Motivated by all these considerations, we include both self-diffusion and cross-diffusion into (1) and study the following system…”

Section: Introductionmentioning

confidence: 99%

“…Each amplitude can be written through a mode ρ j = |A j | and a corresponding phase angle θ j as A j = ρ j exp(iθ j ), j = 1, 2, 3. Substituting in (A13) and separating the real and imaginary parts we get (27).…”

mentioning

confidence: 99%

See 3 more Smart Citations

Cross-Diffusion-Driven Instability in a Predator-Prey System with Fear and Group Defense

Carfora

Torcicollo

2020

Mathematics

View full text Add to dashboard Cite

In this paper, a reaction-diffusion prey-predator system including the fear effect of predator on prey population and group defense has been considered. The conditions for the onset of cross-diffusion-driven instability are obtained by linear stability analysis. The technique of multiple time scales is employed to deduce the amplitude equation near Turing bifurcation threshold by choosing the cross-diffusion coefficient as a bifurcation parameter. The stability analysis of these amplitude equations leads to the identification of various Turing patterns driven by the cross-diffusion, which are also investigated through numerical simulations.

show abstract

Section: Weakly Nonlinear Analysismentioning

confidence: 99%

Section: Weakly Nonlinear Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

Cross-Diffusion-Driven Instability in a Predator-Prey System with Fear and Group Defense

Carfora

Torcicollo

2020

Mathematics

View full text Add to dashboard Cite

show abstract

“…The dynamical behavior of the predator-prey system is one of the main research topics in mathematical ecology and theoretical biology [1][2][3][4][5][6][7][8][9]. Functional response is the core component of the community and food web model, and their mathematical form strongly affects the dynamics and stability of the ecosystem [10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Dynamics of Stage-Structured Predator–Prey Model with Beddington–DeAngelis Functional Response and Harvesting

Cheng

2021

Mathematics

View full text Add to dashboard Cite

In this paper, we investigate the stability of equilibrium in the stage-structured and density-dependent predator–prey system with Beddington–DeAngelis functional response. First, by checking the sign of the real part for eigenvalue, local stability of origin equilibrium and boundary equilibrium are studied. Second, we explore the local stability of the positive equilibrium for τ=0 and τ≠0 (time delay τ is the time taken from immaturity to maturity predator), which shows that local stability of the positive equilibrium is dependent on parameter τ. Third, we qualitatively analyze global asymptotical stability of the positive equilibrium. Based on stability theory of periodic solutions, global asymptotical stability of the positive equilibrium is obtained when τ=0; by constructing Lyapunov functions, we conclude that the positive equilibrium is also globally asymptotically stable when τ≠0. Finally, examples with numerical simulations are given to illustrate the obtained results.

show abstract

Impact of hunting cooperation in predator and anti‐predator behaviors in prey in a predator–prey model

Li,

Ding

2024

Math Methods in App Sciences

View full text Add to dashboard Cite

In this paper, we propose a predator–prey model with hunting cooperation in predator and anti‐predator behaviors in prey. The conditions for the existence and the stability of the unique positive constant equilibrium are given. It is found that with the increasing of the birth rate of the prey, the trivial solution loses its stability, and the semi‐trivial solution emerges and also loses its stability. For the positive constant solution, we find that as the hunting cooperation in predator increases or the fear decreases, the positive constant equilibrium loses its stability, and Hopf bifurcation occurs. We also derive the existence of limit cycles by Poincaré‐Bendixson theorem. We also study a diffusive model and derive that self‐diffusion can induce Turing instability. Finally, we conduct numerical simulations to present our conclusions.

show abstract

Stability and cross-diffusion-driven instability in a diffusive predator–prey system with hunting cooperation functional response

Cited by 42 publications

References 44 publications

Cross-Diffusion-Driven Instability in a Predator-Prey System with Fear and Group Defense

Cross-Diffusion-Driven Instability in a Predator-Prey System with Fear and Group Defense

Dynamics of Stage-Structured Predator–Prey Model with Beddington–DeAngelis Functional Response and Harvesting

Impact of hunting cooperation in predator and anti‐predator behaviors in prey in a predator–prey model

Contact Info

Product

Resources

About