Steady state for a predator–prey cross-diffusion system with the Beddington–DeAngelis and Tanner functional response

Luo, Demou

doi:10.1186/s13661-020-01469-3

Cited by 5 publications

(3 citation statements)

References 15 publications

(15 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In recent years, great attention has been paid to the predator-prey system, which has important application in biological model. Many scholars have carried out the study of different predator-prey models (see [1][2][3][4][5][6]). Among the variety of models, the predator-prey models with different Holling type functional response are refined so as to better reflect the specific characteristics of the different populations or economical needs.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear dynamics in a discrete-time predator-prey system

Liu

2022

Preprint

View full text Add to dashboard Cite

In this article, the nonlinear dynamics of a discrete-time predator-prey system with simplified Holling type IV functional response are reported. Possible codimension-two bifurcations (1:2, 1:3 and 1:4 strong resonances) are investigated under variation of two parameters for certain critical values. For each bifurcation, normal form coefficients along with its scenario are investigated thoroughly. Besides, the numerical simulations have been done, in addition to supporting the analytical findings, more behaviors are extracted from the model, such as fractal structures, mode-locking structures, etc. Our results generate and improve some known results and show that the discrete model has richer dynamics than the continuous one.

show abstract

Section: Introductionmentioning

confidence: 99%

Nonlinear dynamics in a discrete-time predator-prey system

Liu

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…In ecological competition systems, the interaction between populations is usually reflected by functional response functions. Results have shown that the predation relationship between populations greatly affects the dynamic behavior of predatorprey systems (see [6][7][8]). In fact, with the development of the economy, humans will harvest biological populations and develop related biological resources to obtain economic benefits, such as fisheries, forestry, and wildlife management (see [9][10][11]).…”

Section: Introductionmentioning

confidence: 99%

Spatiotemporal Evolution Characteristics of Time-Delay Ecological Competition Systems with Food-Limited and Diffusion

et al. 2022

View full text Add to dashboard Cite

In this paper, we put forward a time-delay ecological competition system with food restriction and diffusion terms under Neumann boundary conditions. For the case without delay, the conditions for local asymptotic stability and Turing instability are constructed. For the case with delay, the existence of Hopf bifurcation is demonstrated by analyzing the root distribution of the corresponding characteristic equations. Furthermore, by using the normal form theory and the center manifold reduction of partial functional differential equations, explicit formulas are obtained to determine the direction of bifurcations and the stability of bifurcating periodic solutions. Finally, some simulation examples are provided to substantiate our analysis.

show abstract

“…The existence of all possible non‐hyperbolic positive equilibria and the dissipativity of the system are studied in this paper. Spatiotemporal dynamics of a prey–predator model with a Holling type III functional response involving Allee effect in prey and hunting cooperation in predator has been studied in Yadav et al 5 Luo 6 studied the existence of non‐constant positive steady states for a cross‐diffusion prey–predator system with the Beddington–DeAngelis and the Tanner functional response by the fixed point index theory. Cao et al 7 investigated the Turing instability and positive steady‐state solutions for a nonlinear cross‐diffusion prey–predator system under the Neumann boundary condition.…”

Section: Introductionmentioning

confidence: 99%

Steady‐state bifurcation and Hopf bifurcation in a cross‐diffusion prey–predator system with Ivlev functional response

Farshid

Jalilian

2022

Math Methods in App Sciences

View full text Add to dashboard Cite

In this paper, we investigate bifurcations of stationary solutions of a cross‐diffusion prey–predator system with Ivlev functional response and Neumann boundary conditions. First, we analyze the local stability and existence of a Hopf bifurcation at a coexistence stationary solution. We show that the bifurcating periodic solutions are asymptotically orbitally stable and the bifurcation direction is supercritical when the ratio of the conversion of prey captured by predator to the death rate of predator is in the interval . Next, we derive sufficient conditions for the existence of a steady‐state bifurcation from a simple eigenvalue. We establish the existence of two intersecting curves of steady‐state solutions near the coexistence stationary solution. To illustrate our theoretical results, we give some numerical examples. From numerical simulations we observe that the coexistence stationary solution loses its stability via the Hopf bifurcation and a periodic solution emerges after a short time. Also by taking the bifurcation parameter value in the stable region, the effect of the initial condition disappears over time and the solution returns to the coexistence stationary solution.

show abstract

Steady state for a predator–prey cross-diffusion system with the Beddington–DeAngelis and Tanner functional response

Cited by 5 publications

References 15 publications

Nonlinear dynamics in a discrete-time predator-prey system

Nonlinear dynamics in a discrete-time predator-prey system

Spatiotemporal Evolution Characteristics of Time-Delay Ecological Competition Systems with Food-Limited and Diffusion

Steady‐state bifurcation and Hopf bifurcation in a cross‐diffusion prey–predator system with Ivlev functional response

Contact Info

Product

Resources

About