Spatiotemporal dynamics induced by nonlocal competition in a diffusive predator-prey system with habitat complexity

Yang, Ruizhi; Nie, Chenxuan; Jin, Dan

doi:10.1007/s11071-022-07625-x

Cited by 36 publications

(3 citation statements)

References 33 publications

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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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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 recent years, many reaction-diffusion equations with nonlocal competition have been used in ecological system modeling [29][30][31][32]. Research indicates that introducing nonlocal effects may lead to the emergence of multi-peaked population density distributions [32][33][34].…”

Section: Introductionmentioning

confidence: 99%

Spatiotemporal Dynamics of a Diffusive Immunosuppressive Infection Model with Nonlocal Competition and Crowley–Martin Functional Response

Xue,

Xu,

Ding

2023

Axioms

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In this paper, we introduce the Crowley–Martin functional response and nonlocal competition into a reaction–diffusion immunosuppressive infection model. First, we analyze the existence and stability of the positive constant steady states of the systems with nonlocal competition and local competition, respectively. Second, we deduce the conditions for the occurrence of Turing, Hopf, and Turing–Hopf bifurcations of the system with nonlocal competition, as well as the conditions for the occurrence of Hopf bifurcations of the system with local competition. Furthermore, we employ the multiple time scales method to derive the normal forms of the Hopf bifurcations reduced on the center manifold for both systems. Finally, we conduct numerical simulations for both systems under the same parameter settings, compare the impact of nonlocal competition, and find that the nonlocal term can induce spatially inhomogeneous stable periodic solutions. We also provide corresponding biological explanations for the simulation results.

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“…In nonlinear systems covering ecology, economics, sociology and many other fields, complex dynamic evolutionary behaviors, such as multiplicity, self-oscillation, and even chaos arise in the vicinity of bifurcation points [ 1 ], and various methods are adopted to enhance sensory ability for accurate manipulation and control: the bifurcation oscillator is applied as a quantum state amplifier [ 2 ], the oscillating clearance of the rolling-element bear is taken as the bifurcating parameter with repetitive errors fused into the control system [ 3 ], and deep learning is implemented for the control of the Van del Pol system [ 4 ]. Mathematically, a bifurcation takes place at a parameter value where the system loses structural stability with respect to parameter variations, i.e., a phase portrait around the equilibrium is not locally topologically conjugate to the phase portraits around the equilibrium at nearby parameter values [ 5 , 6 ], which leads the solution manifold to change significantly, and exacerbates system information acquisition and control implementation [ 7 , 8 ].…”

Section: Introductionmentioning

confidence: 99%

Bifurcation Control on the Un-Linearizable Dynamic System via Washout Filters

Zhai

Yang

2022

Sensors

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Information fusion integrates aspects of data and knowledge mostly on the basis that system information is accumulative/distributive, but a subtle case emerges for a system with bifurcations, which is always un-linearizable and exacerbates information acquisition and presents a control problem. In this paper, the problem of an un-linearizable system related to system observation and control is addressed, and Andronov–Hopf bifurcation is taken as a typical example of an un-linearizable system and detailed. Firstly, the properties of a linear/linearized system is upon commented. Then, nonlinear degeneracy for the normal form of Andronov–Hopf bifurcation is analyzed, and it is deduced that the cubic terms are an integral part of the system. Afterwards, the theoretical study on feedback stabilization is conducted between the normal-form Andronov–Hopf bifurcation and its linearized counterpart, where stabilization using washout-filter-aided feedback is compared, and it is found that by synergistic controller design, the dual-conjugate-unstable eigenvalues can be stabilized by single stable washout filter. Finally, the high-dimensional ethanol fermentation model is taken as a case study to verify the proposed bifurcation control method.

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Spatiotemporal dynamics induced by nonlocal competition in a diffusive predator-prey system with habitat complexity

Cited by 36 publications

References 33 publications

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

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

Spatiotemporal Dynamics of a Diffusive Immunosuppressive Infection Model with Nonlocal Competition and Crowley–Martin Functional Response

Bifurcation Control on the Un-Linearizable Dynamic System via Washout Filters

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