Fractional-order PD control at Hopf bifurcation in a delayed predator–prey system with trans-species infectious diseases

Du, Wentong; Xiao, Min; Ding, Jie; Yao, Yi; Wang, Zhengxin; Yang, Xiaoguang

doi:10.1016/j.matcom.2022.10.014

Cited by 22 publications

(6 citation statements)

References 40 publications

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“…During the past several decades, numerous controllers to control the bifurcation of fractional-order differential systems have been developed. In this section, we adopt a hybrid controller relying on the viewpoint of [31]. This controller includes state feedback and parameter perturbation concerning delay.…”

Section: Hybrid Controller Design For Hopf Bifurcationmentioning

confidence: 99%

Bifurcation Exploration and Controller Design in a Fractional Oxygen–Plankton Model with Delay

Zhang,

2024

Fractal Fract

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Fractional-order differential equations have been proved to have great practical application value in characterizing the dynamical peculiarity in biology. In this article, relying on earlier work, we formulate a new fractional oxygen–plankton model with delay. First of all, the features of the solutions of the fractional delayed oxygen–plankton model are explored. The judgment rules on non-negativeness, existence and uniqueness and the boundedness of the solution are established. Subsequently, the generation of bifurcation and stability of the model are dealt with. Delay-independent parameter criteria on bifurcation and stability are presented. Thirdly, a hybrid controller and an extended hybrid controller are designed to control the time of onset of bifurcation and stability domain of this model. The critical delay value is provided to display the bifurcation point. Last, software experiments are offered to support the acquired key outcomes. The established outcomes of this article are perfectly innovative and provide tremendous theoretical significance in balancing the oxygen density and the phytoplankton density in biology.

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Section: Hybrid Controller Design For Hopf Bifurcationmentioning

confidence: 99%

Bifurcation Exploration and Controller Design in a Fractional Oxygen–Plankton Model with Delay

Zhang,

2024

Fractal Fract

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“…Mathematical models given by ordinary differential equations (ODEs) [1,2] are used to describe the time evolution of dynamical systems in many branches of science. The ODEs model different dynamical phenomena that originate from mechanical engineering [3][4][5], neuroscience [6,7], physics [8][9][10][11], medicine [12,13], electromechanics [14,15], production technologies [16,17], ecology [18,19], biology [20][21][22][23], climate dynamics [24,25], and many more. Still, every case may require a different approach for dynamical analysis.…”

Section: Introductionmentioning

confidence: 99%

A Unified Approach for the Calculation of Different Sample-Based Measures with the Single Sampling Method

Leszczynski,

Perlikowski,

Brzeski

2024

Mathematics

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This paper explores two sample-based methods for analysing multistable systems: basin stability and basin entropy. Both methods rely on many numerical integration trials conducted with diverse initial conditions. The collected data is categorised and used to compute metrics that characterise solution stability, phase space structure, and system dynamics predictability. Basin stability assesses the overall likelihood of reaching specific solutions, while the basin entropy measure aims to capture the structure of attraction basins and the complexity of their boundaries. Although these two metrics complement each other effectively, their original procedures for computation differ significantly. This paper introduces a universal approach and algorithm for calculating basin stability and entropy measures. The suitability of these procedures is demonstrated through the analysis of two non-linear systems.

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“…Research in this interdisciplinary field has not only expanded our understanding of the life sciences but has also had a profound impact on practical applications such as medicine, ecology, and agriculture. Among them, many researchers [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] focus on the study of predator-prey systems in biomathematics. The study of predator-prey systems not only contributes to the development of scientific theories, but is also directly related to the sustainable development of human society and the health of ecosystems.…”

Section: Introductionmentioning

confidence: 99%

Hopf Bifurcation and Control for the Bioeconomic Predator–Prey Model with Square Root Functional Response and Nonlinear Prey Harvesting

Guo,

Han,

Zhang

2023

Mathematics

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In this essay, we introduce a bioeconomic predator–prey model which incorporates the square root functional response and nonlinear prey harvesting. Due to the introduction of nonlinear prey harvesting, the model demonstrates intricate dynamic behaviors in the predator–prey plane. Economic profit serves as a bifurcation parameter for the system. The stability and Hopf bifurcation of the model are discussed through normal forms and bifurcation theory. These results reveal richer dynamic features of the bioeconomic predator–prey model which incorporates the square root functional response and nonlinear prey harvesting, and provides guidance for realistic harvesting. A feedback controller is introduced in this paper to move the system from instability to stability. Moreover, we discuss the biological implications and interpretations of the findings. Finally, the results are validated by numerical simulations.

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Fractional-order PD control at Hopf bifurcation in a delayed predator–prey system with trans-species infectious diseases

Cited by 22 publications

References 40 publications

Bifurcation Exploration and Controller Design in a Fractional Oxygen–Plankton Model with Delay

Bifurcation Exploration and Controller Design in a Fractional Oxygen–Plankton Model with Delay

A Unified Approach for the Calculation of Different Sample-Based Measures with the Single Sampling Method

Hopf Bifurcation and Control for the Bioeconomic Predator–Prey Model with Square Root Functional Response and Nonlinear Prey Harvesting

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