DYNAMICS OF A DIFFUSIVE SINGLE-SPECIES MODEL WITH NONLOCALITY AND DISTRIBUTED MEMORY

Shuhao Wu; Xin Lu

doi:10.11948/20250093

2025 Volume 15 Issue 6

Article Contents

Article navigation > Journal of Applied Analysis & Computation > 2025 > 15(6): 3751-3768

Next Article Previous Article

Shuhao Wu, Xin Lu. DYNAMICS OF A DIFFUSIVE SINGLE-SPECIES MODEL WITH NONLOCALITY AND DISTRIBUTED MEMORY[J]. Journal of Applied Analysis & Computation, 2025, 15(6): 3751-3768. doi: 10.11948/20250093

Citation:

Shuhao Wu, Xin Lu. DYNAMICS OF A DIFFUSIVE SINGLE-SPECIES MODEL WITH NONLOCALITY AND DISTRIBUTED MEMORY[J]. Journal of Applied Analysis & Computation, 2025, 15(6): 3751-3768. doi: 10.11948/20250093

DYNAMICS OF A DIFFUSIVE SINGLE-SPECIES MODEL WITH NONLOCALITY AND DISTRIBUTED MEMORY

Shuhao Wu^1, ,,
Xin Lu^1,

1.
School of Mathematics, Foshan University, Foshan 528000, China

Author Bio: Email: luxin1024@126.com(X. Lu)
Corresponding author: Email: swu@fosu.edu.cn(S. Wu)
Fund Project: Shuhao Wu was supported by National Natural Science Foundation of China (No. 12201117)

Abstract

Abstract

Cognitive abilities and memorized information are significant for "smart" animals to make movement decisions. This work establishes a diffusive single-species model with nonlocality and distributed memory. We consider weak and strong temporal kernels in the memory-based diffusion term and find that the model exhibits complex dynamical behaviour produced by nonlocality and distributed memory. For either temporal kernel, mode-n Turing (or Hopf) bifurcation can emerge and double Turing bifurcation can be generated by mode-n and mode-m ($ n\neq m $) Turing bifurcations. Additionally, Hopf bifurcation is possible to occur for small random diffusion or large repulsive memory-based diffusion in considerations of weak or strong kernels, respectively. Note that the critical Turing bifurcation curve can be mode-n ($ n\geq2 $), which differs from that in the model with nonlocal spatial average, while Turing, Turing-Hopf and double Turing bifurcations do not appear in the single-species model involving only distributed memory delay. An application to our theoretical findings is presented and Turing-Hopf bifurcation and stability switches are found in numerical exploration by considering weak and strong kernels, respectively.
- Nonlocality /
- distributed memory /
- Turing bifurcation /
- Hopf bifurcation
MSC: 35B32, 37G05, 92D25

FullText(HTML)

References

[1]	N. Britton, Aggregation and the competitive exclusion principle, J. Theor. Biol., 1989, 136(1), 57-66. doi: 10.1016/S0022-5193(89)80189-4 CrossRef Google Scholar
[2]	S. Chen and J. Shi, Global attractivity of equilibrium in gierer-meinhardt system with activator production saturation and gene expression time delays, Nonlinear Anal. -Real World Appl., 2013, 14(4), 1871-1886. Google Scholar
[3]	W. F. Fagan, M. A. Lewis, M. Auger-Méthé and T. Avgar, Spatial memory and animal movement, Ecology Letters, 2013, 16(10), 1316-1329. Google Scholar
[4]	H. Hochstadt, Integral Equations, Wiley Interscience, New York, 1973. Google Scholar
[5]	Q. Ji, R. Wu and T. Zhang, Dynamics of a single population model with memory and nonlinear boundary condition, Appl. Anal., 2024. DOI: 10.1080/00036811.2024.2426229. CrossRef Google Scholar
[6]	J. Lin and Y. Song, Spatially inhomogeneous periodic patterns induced by distributed memory in the memory-based single population model, Appl. Math. Lett., 2023, 137, 108490. doi: 10.1016/j.aml.2022.108490 CrossRef Google Scholar
[7]	W. Ni, J. Shi and M. Wang, Global stability and pattern formation in a nonlocal diffusive Lotka-Volterra competition model, J. Differ. Equ., 2018, 264(11), 6891-6932. doi: 10.1016/j.jde.2018.02.002 CrossRef Google Scholar
[8]	F. Riez and B. Sz-Nagy, Functional Analysis, Ungar, New York, 1955. Google Scholar
[9]	U. E. Schläegel and M. A. Lewis, Detecting effects of spatial memory and dynamic information on animal movement decisions, Methods Ecol. Evol., 2014, 5(11), 1236-1246. doi: 10.1111/2041-210X.12284 CrossRef Google Scholar
[10]	H. Shen and Y. Song, Spatiotemporal patterns in a diffusive resource-consumer model with distributed memory and maturation delay, Math. Comput. Simul., 2024, 221, 622-644. doi: 10.1016/j.matcom.2024.03.026 CrossRef Google Scholar
[11]	H. Shen, Y. Song and H. Wang, Bifurcations in a diffusive resource-consumer model with distributed memory, J. Differ. Equ., 2023, 347, 170-211. doi: 10.1016/j.jde.2022.11.044 CrossRef Google Scholar
[12]	J. Shi and Q. Shi, Spatial movement with temporally distributed memory and dirichlet boundary condition, J. Differ. Equ., 2024, 389, 305-337. doi: 10.1016/j.jde.2024.01.022 CrossRef Google Scholar
[13]	J. Shi, C. Wang and H. Wang, Diffusive spatial movement with memory and maturation delays, Nonlinearity, 2019, 32(9), 3188-3208. doi: 10.1088/1361-6544/ab1f2f CrossRef Google Scholar
[14]	J. Shi, C. Wang, H. Wang and X. Yan, Diffusive spatial movement with memory, J. Dynam. Differential Equations, 2020, 32(2), 979-1002. doi: 10.1007/s10884-019-09757-y CrossRef Google Scholar
[15]	Q. Shi, J. Shi and H. Wang, Spatial movement with distributed memory, J. Math. Biol., 2021, 82(4), 33. Google Scholar
[16]	Y. Song, S. Wu and H. Wang, Memory-based movement with spatiotemporal distributed delays in diffusion and reaction, Appl. Math. Comput., 2021, 404, 126254. Google Scholar
[17]	D. Wang and C. Wang, Dynamics of a diffusive two-species interaction model with memory effect, Discrete Contin. Dyn. Syst. -Ser. B, 2024. DOI: 10.3934/dcdsb.2024187. CrossRef Google Scholar
[18]	S. Wu and Y. Song, Spatial movement with distributed memory and maturation delay, Qual. Theor. Dyn. Syst., 2024, 23(3), 117. Google Scholar