On the stability and Hopf-bifurcation of a multi-delayed competitive population system affected by toxic substances with imprecise biological parameters

Jana, Dipak Kumar; Dolai, P.; Pal, A. K.; Samanta, G. P.

doi:10.1007/s40808-016-0156-0

Cited by 12 publications

(5 citation statements)

References 27 publications

(19 reference statements)

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“…At present, some literatures, such as [3,4,8,11,14,[16][17][18][19][22][23][24][25][26], have studied the effects of toxins on different ecosystem species. [4] indicated that once some external toxic substances directly infected the prey, then the predator consuming polluted prey was indirectly influenced by the toxicant.…”

Section: Introductionmentioning

confidence: 99%

Spatiotemporal dynamics in a toxin-producing predator–prey model with threshold harvesting

Ye¹,

Zhao²,

Wu³

2023

NAMC

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In this paper, we propose a toxin-producing predator–prey model with threshold harvesting and study spatiotemporal dynamics of the model under the homogeneous Neumann boundary conditions. At first, the persistence property of solutions to the system is investigated. Then the explicit requirements for the existence of nonconstant steady state solutions are derived by studying the relevant characteristic equation. These steady states occur from related constant steady states via steady state bifurcation. Throughout the analysis of the amplitude equations of Turing pattern by the multiple scale method, pattern formation can be found. Finally, we display umericalsimulations to verify the theoretical outcomes.

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Section: Introductionmentioning

confidence: 99%

Spatiotemporal dynamics in a toxin-producing predator–prey model with threshold harvesting

Ye¹,

Zhao²,

Wu³

2023

NAMC

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“…Hallam and Clark [6], Hallam et al [7], Hallam and De Luna [8] started eco-toxicological modeling through mathematics. In this context it is mentioned that De Luna and Hallam [13], Freedman and Shukla [5], Samanta [23], Shukla and Dubey [24] and others [10,17,21] have made important contributions on this field. However, most of these models recognize with single species or two-species ecological communities.…”

Section: Introductionmentioning

confidence: 99%

“…In recent time, mathematically modeling of eco-toxicological problems in aquatic environment are extensively studied by several researchers. They are paying attention on the eco-toxicological effects of toxic substances released by the marine biological species themselves [10,17,20,21,23].…”

Section: Introductionmentioning

confidence: 99%

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A system of two competitive prey species in presence of predator under the influence of toxic substances

Mondal

Pal

Dolai

et al. 2022

Filomat

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In this article, a two prey - one predator model has been studied where two prey species are competitive in nature and also uses toxic substances for own existence. Biologically well posedness of the model system has been shown through positivity and boundedness of solutions. Existence criterion and stability analysis of the non-negative equilibrium points have been discussed. The sufficient conditions for existence of Hopf bifurcation and stability switches induced by delay are investigated. The direction and the stability criteria of the bifurcating periodic solutions are determined with the help of the normal form theory and the center manifold theorem. Numerical simulations are performed to illustrate the theoretical analysis results.

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“…e competition-cooperation relationship widely exists in the real enterprise clusters and has a major impact on the evolution of enterprise clusters [5][6][7][8][9]. To study the influence of competition and cooperation on the evolution of enterprise clusters, researchers propose a competition-cooperation enterprise cluster model [10] based on the ecology model [11][12][13][14][15], which is described as follows:…”

Section: Introductionmentioning

confidence: 99%

Dynamic Analysis of a Competition‐Cooperation Enterprise Cluster with Core‐Satellite Structure and Time Delay

Dong

Zhao

2021

Complexity

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Core and satellite structure is one of the common structures in enterprise clusters. In core and satellite structure, there are one core enterprise and at least two satellite enterprises. There exist a competitive relationship between satellite enterprises and a cooperative relationship between satellite enterprise and core enterprise. However, the dynamic evolution of competition-cooperation enterprise clusters with core-satellite structure is not well understood. In this paper, a novel competition-cooperation enterprise cluster model with core-satellite structure is proposed. The boundedness of the positive equilibrium is investigated. It is found that there exists upper bound of both core enterprise output and satellite enterprise output and the upper bound of core enterprise not only depends on its own production capacity but also depends on the production capacity of two satellite enterprises. Then, by selecting the production period as bifurcating parameter, the conditions of local stability and Hopf bifurcation are obtained. Once the production period passes a critical value, the output of both core enterprise and satellite enterprise loses stability and displays periodic fluctuations. This may lead to the decline of efficiency of enterprise and resource mismatch. Furthermore, the fluctuation properties are studied. Finally, a numerical example is presented to show the effectiveness of theorem.

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On the stability and Hopf-bifurcation of a multi-delayed competitive population system affected by toxic substances with imprecise biological parameters

Cited by 12 publications

References 27 publications

Spatiotemporal dynamics in a toxin-producing predator–prey model with threshold harvesting

Spatiotemporal dynamics in a toxin-producing predator–prey model with threshold harvesting

A system of two competitive prey species in presence of predator under the influence of toxic substances

Dynamic Analysis of a Competition‐Cooperation Enterprise Cluster with Core‐Satellite Structure and Time Delay

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