Hopf–Zero bifurcation in an age-dependent predator–prey system with Monod–Haldane functional response comprising strong Allee effect

Yang, Peng; Wang, Yuanshi

doi:10.1016/j.jde.2020.06.048

Cited by 15 publications

(14 citation statements)

References 15 publications

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“…Compared with the models proposed in [1][2][3][4][5], model ( 6) is a new measure of the population with a nonlinear average growth rate based on food restriction. At the same time, we consider the reaction-diffusion factors for system (6) to study their influence on the dynamic behaviors of systems. In addition, on the basis of references [16][17][18][19][20], we introduce the nonlinear harvesting term of the harvesting-effort coefficient E into system (6) and study the stability and related dynamic characteristics of the system under Holling I and Holling II functional response functions.…”

Section: Lemmamentioning

confidence: 99%

“…At the same time, we consider the reaction-diffusion factors for system (6) to study their influence on the dynamic behaviors of systems. In addition, on the basis of references [16][17][18][19][20], we introduce the nonlinear harvesting term of the harvesting-effort coefficient E into system (6) and study the stability and related dynamic characteristics of the system under Holling I and Holling II functional response functions. Importantly, the addition of pregnancy delay can more accurately reflect the evolution of the population and make the system show more complex dynamic characteristics than the model without delay, which is also a widely concerned direction in the research of biological systems.…”

Section: Lemmamentioning

confidence: 99%

“…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%

See 2 more Smart Citations

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

et al. 2022

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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.

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Section: Lemmamentioning

confidence: 99%

Section: Lemmamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

et al. 2022

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“…It is assumed that the biomass conversion of predator is expressed by square root functional response which both predator and prey with schooling behaviour. Recently, the Allee effect has been introduced in the growth of population widely [3,4,20,28,35,36,42]. Allee [2] proposed the Allee effect, which mainly divided into two classes: strong and weak [35].…”

Section: Introductionmentioning

confidence: 99%

Dynamical analysis of a delayed diffusive predator–prey model with schooling behaviour and Allee effect

Meng

Jiao-guo

2020

Journal of Biological Dynamics

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In this paper, a delayed diffusive predator-prey model with schooling behaviour and Allee effect is investigated. The existence and local stability of equilibria of model without time delay and diffusion are given. Regarding the conversion rate as bifurcation parameter, Hopf bifurcation of diffusive system without time delay is obtained. In addition, the local stability of the coexistent equilibrium and existence of Hopf bifurcation of system with time delay are discussed. Moreover, the properties of Hopf bifurcation are studied based on the centre manifold and normal form theory for partial functional differential equations. Finally, some numerical simulations are also carried out to confirm our theoretical results.

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“…Hence, many scholars have made strenuous efforts, so as to find out the impact of age on evolution. For more details, please see [29,19,12,1,28,23,35,36,30,31,10,34,37,33,32] and the references therein for related works. Unfortunately, most of these equations barely get the existence, boundedness and positivity of the solution for the age-dependent version predation equations.…”

mentioning

confidence: 99%

On oscillations to a 2D age-dependent predation equations characterizing Beddington-DeAngelis type schemes

Yang

Wang

2022

DCDS-B

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<p style='text-indent:20px;'>In this study, a 2D age-dependent predation equations characterizing Beddington<inline-formula><tex-math id="M1">\begin{document}$ - $\end{document}</tex-math></inline-formula>DeAngelis type schemes are established to investigate the evolutionary dynamics of population, in which the predator is selected to be depicted with an age structure and its fertility function is assumed to be a step function. The dynamic behaviors of the equations are derived from the integrated semigroup method, the Hopf bifurcation theorem, the center manifold reduction and normal form theory of semilinear equations with non-dense domain. It turns out that the equations appear the oscillation phenomenon via Hopf bifurcation (positive equilibrium age distribution lose its stability and give rise to periodic solutions), as the bifurcation parameter moves across certain threshold values. Additionally, the explicit expressions are offered to determine the properties of Hopf bifurcation (the direction the Hopf bifurcation and the stability of the bifurcating periodic solutions). This technique can also be employed to other epidemic and ecological equations. Eventually, some numerical simulations and conclusions are executed to validating the major results of this work.</p>

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Hopf–Zero bifurcation in an age-dependent predator–prey system with Monod–Haldane functional response comprising strong Allee effect

Cited by 15 publications

References 15 publications

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

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

Dynamical analysis of a delayed diffusive predator–prey model with schooling behaviour and Allee effect

On oscillations to a 2D age-dependent predation equations characterizing Beddington-DeAngelis type schemes

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