Traveling wave fronts of a diffusive Nicholson’s Blowflies equation with two delays

Huang, Lizhuang; Xu, Zhiting

doi:10.1016/j.aml.2022.108545

Cited by 5 publications

(2 citation statements)

References 10 publications

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“…Weak solutions can model the spread of cancer in the body, the dynamics of populations of competing species, and the spread of viruses and other diseases in populations (see [12,18,30]). In mathematical biology, the existence of traveling wave front solution and analysis for Nicholson's blowflies equation are studied in [14] and [15]. The finite-time stability for cellular neural networks with neutral proportional delays and time-varying leakage delays are studied by using the differential inequality technique in [19].…”

Section: Introductionmentioning

confidence: 99%

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On the unique weak solvability of second-order unconditionally stable difference scheme for the system of sine-Gordon equations

Yildirim

2024

NAMC

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In the present paper, a nonlinear system of sine-Gordon equations that describes the DNA dynamics is considered. A novel unconditionally stable second-order accuracy difference scheme corresponding to the system of sine-Gordon equations is presented. In this work, for the first time in the literature, weak solution of this difference scheme is studied. The existence and uniqueness of the weak solution for the difference scheme are proved in the space of distributions, and the methods of variational calculus are applied. The finite-difference method and the fixed point theory are used in combination to perform numerical experiments that verify the theoretical statements.

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Section: Introductionmentioning

confidence: 99%

“…The weak and global solutions, nonlinear dynamics of PDEs, finite-difference and finite-element methods are extensively studied by many scientists (see [1,6,[13][14][15][16][17][18][19][20][21][22][23]28,32] and the references given therein).…”

Section: Introductionmentioning

confidence: 99%

On the unique weak solvability of second-order unconditionally stable difference scheme for the system of sine-Gordon equations

Yildirim

2024

NAMC

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Spatial propagation in a delayed spruce budworm diffusive model

Huang,

2024

Math Methods in App Sciences

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We investigate the spatial propagation in a delayed spruce budworm diffusive model where and represent, respectively, the incubation and the maturation delays for the spruce budworm. We find the minimal wave speed to determine the existence of traveling wave fronts of the model. More specifically, the model admits traveling wave fronts when ; the model has no traveling wave solutions when . The proofs are based on combining the upper and lower solutions with the approach of Wu and Zou's theorems, the limit arguments, and Laplace transform. The obtained results help us to understand the spreading patterns and the spreading speed of spruce budworm population.

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Dynamics of the diffusive Nicholson’s blowflies equation with two distinct distributed delays

Huang

Ding

2023

Applied Mathematics Letters

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Traveling wave fronts of a diffusive Nicholson’s Blowflies equation with two delays

Cited by 5 publications

References 10 publications

On the unique weak solvability of second-order unconditionally stable difference scheme for the system of sine-Gordon equations

On the unique weak solvability of second-order unconditionally stable difference scheme for the system of sine-Gordon equations

Spatial propagation in a delayed spruce budworm diffusive model

Dynamics of the diffusive Nicholson’s blowflies equation with two distinct distributed delays

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