Stability and Hopf bifurcation of a heterogeneous diffusive model with spatial memory

Ji, Quanli; Wu, Ranchao

doi:10.3934/dcdsb.2023176

DCDS-B

2024

DOI: 10.3934/dcdsb.2023176

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Stability and Hopf bifurcation of a heterogeneous diffusive model with spatial memory

Quanli Ji,

Ranchao Wu

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2024

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Cited by 3 publications

References 37 publications

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Dynamics of a single population model with memory and nonlinear boundary condition

Ji,

Wu,

Zhang

2024

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Dynamics of a single population model with memory and nonlinear boundary condition

Ji,

Wu,

Zhang

2024

Applicable Analysis

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Dynamics of a Memory‐Based Diffusion Model With Maturation Delay and Spatial Heterogeneity

Bu,

Zhang,

Song

et al. 2024

Stud Appl Math

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In this paper, we consider a single memory‐based diffusion population model with maturation delay, spatial heterogeneity, and Neumann boundary condition. When the integral of the intrinsic growth rate over the domain is nonnegative, we obtain sufficient conditions for the local stability of the positive steady state and the critical values of maturation delay for the associated Hopf bifurcation. When the integral of the intrinsic growth rate over the domain is negative, considering that the characteristic equation involves a non‐self‐adjoint operator and two delays, we utilize a geometric method to determine all bifurcation points in terms of memory and maturation delays. The impact of spatial heterogeneity on the distribution of solutions is also examined via numerical simulations. It is found that the core area of high population density is coincident with the source area of growth rate. This suggests the importance of spatial heterogeneity in shaping the distribution and dynamics of the species.

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Stability and bifurcation of a heterogeneous memory-based diffusive model

Ji,

Wu,

Zhang

2024

DCDS-S

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Stability and Hopf bifurcation of a heterogeneous diffusive model with spatial memory

Cited by 3 publications

References 37 publications

Dynamics of a single population model with memory and nonlinear boundary condition

Dynamics of a single population model with memory and nonlinear boundary condition

Dynamics of a Memory‐Based Diffusion Model With Maturation Delay and Spatial Heterogeneity

Stability and bifurcation of a heterogeneous memory-based diffusive model

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