Bifurcations and hydra effects in Bazykin’s predator–prey model

Adhikary, Prabir Das; Mukherjee, Saikat; Ghosh, Bapan

doi:10.1016/j.tpb.2021.05.002

Cited by 19 publications

(9 citation statements)

References 29 publications

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“…The effect of hydra on the differential equation model has been widely studied in the development of science in recent years. The formulated modeling adopts a lot of relevant research (Adhikary et al, 2021). Some of the theoretical studies have been widely expressed, as theories that support the developed model.…”

Section: Methodsmentioning

confidence: 99%

Hydra effects predator-prey bazykin's model with stage-structure and intraspecific for predator

Pratama

Siddik

Dadi

et al. 2022

DJM

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Bazykin's predator-prey population model is considered to represent the exchange stability condition of population growth. The existence of the hydra effect and, at the same time, analyzing its influence on population growth. The condition of the model divides the species into a stage structure, namely, prey, immature predators, and mature predators. The population growth of the three species has its own characteristics. This research revealed that the Holling type II and intraspecific predatory function responses together induce the Hydra effect. In the model formed, there are 12 equilibrium points, with details for every seven points of negative imaginary equilibrium and five points of non-negative equilibrium. The findings of research studies center on five points of non-negative equilibrium. All real roots that interpret the species population's growth conditions are taken and tested for long-term stability. The test results show one point of equilibrium that meets the Routh-Hurwitz criteria and their characteristic equations. In numerical simulations, the maximum sustained yield is in the local asymptotic stable state. The growth of prey trajectories increased significantly, although at the beginning of the interaction there was a slowdown in population growth. Meanwhile, the population of immature predators and mature predators was not significantly different. Both populations grow steadily toward the point of population stability. It turns out that the two populations grow inversely, the faster the rate of predation by predators, the faster the growth rate of the prey population.

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Section: Methodsmentioning

confidence: 99%

Hydra effects predator-prey bazykin's model with stage-structure and intraspecific for predator

Pratama

Siddik

Dadi

et al. 2022

DJM

View full text Add to dashboard Cite

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“…It is supposed that such condition ( 7) is well-done. In addition, the condition (7) and one of following conditions…”

Section: Preliminariesmentioning

confidence: 99%

“…Bazykin [4] presented a variation of Volterra's classical predator-prey model under the help of Michaelis-Menton equation, which can be called Bazykin's predator-prey model according to Bazykin's modi cation. Since then, the Bazykin's predator-prey system has received the attention of a large number of scholars and obtained some excellent research results [5][6][7][8][9][10]. e paper [5] investigated bifurcations of equilibria in Bazykin's predator-prey model.…”

Section: Introductionmentioning

confidence: 99%

“…e paper [6] researched stability and bifurcation of Bazykin's predator-prey model with memory e ect, which can reveal the e ect of memory based growth on global bifurcation threshold. e paper [7] considered Bazykin's predator-prey model to address harvesting induced stability exchanges through bifurcation analysis, which can be useful to understand conservation policy and fishery management. e paper [8] proposed Bazykin predator-prey model with Beddington-DeAngelis response function to study persistence and global stability.…”

Section: Introductionmentioning

confidence: 99%

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Equilibria and Bogdanov‐Takens Bifurcation Analysis in the Bazykin’s Predator‐Prey System

Wang

2022

Discrete Dynamics in Nature and Society

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In the paper, we proposed a Bazykin’s predator-prey system to explore the equilibrium point and Bogdanov-Takens bifurcation problems. Firstly, we derived some key parameter threshold conditions to ensure that the Bazykin’s predator-prey system had a multiple focus of multiplicity one, weak focus of order 2, cusps of codimension 2 and a degenerate Bogdanov-Takens singularity (focus or center case) of codimension 3. Furthermore, the distinction of two types of codimension 2 cusps was also discussed, which showed that the threshold of the two types of cusps could exhibit a cusp, which was a special case of the mentioned degenerate Bogdanov-Takens singularity (focus or center case) of codimension 3. Secondly, we systematically calculated that the Bazykin’s predator-prey system could undergo two types of Bogdanov-Takens bifurcations of codimension 2 and a degenerate focus type Bogdanov-Takens bifurcation of codimension 3. Finally, some numerical examples were implemented to verify the correctness and feasibility of mathematical theory derivation, which also directly showed all possible equilibrium points and Bogdanov-Takens bifurcations of Bazykin’s predator-prey system. In a word, all the research results could play an important theoretical support role in the study of controlling cyanobacteria bloom.

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“…We find that in some of our models, a hydra effect is present (see Conclusions and Discussion). The hydra effect was first noted by Ricker [22] and has later been incorporated in different models; see, e.g., Abrams [20], Adhikary et al [23], and Ghosh et al [24].…”

Section: Introductionmentioning

confidence: 99%

Properties in Stage-Structured Population Models with Deterministic and Stochastic Resource Growth

Aye

Carlsson

2022

Journal of Applied Mathematics

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Modelling population dynamics in ecological systems reveals properties that are difficult to find by empirical means, such as the probability that a population will go extinct when it is exposed to harvesting. To study these properties, we use an aquatic ecological system containing one fish species and an underlying resource as our models. In particular, we study a class of stage-structured population systems with and without starvation. In these models, we study the resilience, the recovery potential, and the probability of extinction and show how these properties are affected by different harvesting rates, both in a deterministic and stochastic setting. In the stochastic setting, we develop methods for deriving estimates of these properties. We estimate the expected outcome of emergent population properties in our models, as well as measures of dispersion. In particular, two different approaches for estimating the probability of extinction are developed. We also construct a method to determine the recovery potential of a species that is introduced in a virgin environment.

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Bifurcations and hydra effects in Bazykin’s predator–prey model

Cited by 19 publications

References 29 publications

Hydra effects predator-prey bazykin's model with stage-structure and intraspecific for predator

Hydra effects predator-prey bazykin's model with stage-structure and intraspecific for predator

Equilibria and Bogdanov‐Takens Bifurcation Analysis in the Bazykin’s Predator‐Prey System

Properties in Stage-Structured Population Models with Deterministic and Stochastic Resource Growth

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