Citation: Anna Sun, Ranchao Wu, Mengxin Chen. Turing-Hopf bifurcation analysis in a diffusive Gierer-Meinhardt model[J]. AIMS Mathematics, 2021, 6(2): 1920-1942. doi: 10.3934/math.2021117
[1] | Ming Wei, Congxin Yang, Bo Sun, Binbin Jing . A multi-objective optimization model for green demand responsive airport shuttle scheduling with a stop location problem. Electronic Research Archive, 2023, 31(10): 6363-6383. doi: 10.3934/era.2023322 |
[2] | Gang Cheng, Changliang He . Analysis of bus travel characteristics and predictions of elderly passenger flow based on smart card data. Electronic Research Archive, 2022, 30(12): 4256-4276. doi: 10.3934/era.2022217 |
[3] | Ming Wei, Shaopeng Zhang, Bo Sun . Comprehensive operating efficiency measurement of 28 Chinese airports using a two-stage DEA-Tobit method. Electronic Research Archive, 2023, 31(3): 1543-1555. doi: 10.3934/era.2023078 |
[4] | Xiaojie Huang, Gaoke Liao . Identifying driving factors of urban digital financial network—based on machine learning methods. Electronic Research Archive, 2022, 30(12): 4716-4739. doi: 10.3934/era.2022239 |
[5] | Jiaqi Chang, Xuhan Xu . Network structure of urban digital financial technology and its impact on the risk of commercial banks. Electronic Research Archive, 2022, 30(12): 4740-4762. doi: 10.3934/era.2022240 |
[6] | Jian Wan, Peiyun Yang, Wenbo Zhang, Yaxing Cheng, Runlin Cai, Zhiyuan Liu . A taxi detour trajectory detection model based on iBAT and DTW algorithm. Electronic Research Archive, 2022, 30(12): 4507-4529. doi: 10.3934/era.2022229 |
[7] | Gang Cheng, Yijie He . Enhancing passenger comfort and operator efficiency through multi-objective bus timetable optimization. Electronic Research Archive, 2024, 32(1): 565-583. doi: 10.3934/era.2024028 |
[8] | Zhenghui Li, Jinhui Zhu, Jiajia He . The effects of digital financial inclusion on innovation and entrepreneurship: A network perspective. Electronic Research Archive, 2022, 30(12): 4697-4715. doi: 10.3934/era.2022238 |
[9] | Jie Ren, Shiru Qu, Lili Wang, Yu Wang, Tingting Lu, Lijing Ma . Research on en route capacity evaluation model based on aircraft trajectory data. Electronic Research Archive, 2023, 31(3): 1673-1690. doi: 10.3934/era.2023087 |
[10] | Yaxi Xu, Yi Liu, Ke Shi, Xin Wang, Yi Li, Jizong Chen . An airport apron ground service surveillance algorithm based on improved YOLO network. Electronic Research Archive, 2024, 32(5): 3569-3587. doi: 10.3934/era.2024164 |
[1] |
A. M. Turing, The chemical basis of morphogenesis, Philos. Trans. R. Soc. Lond. B, 237 (1952), 37-72. doi: 10.1098/rstb.1952.0012
![]() |
[2] |
A. Gierer, H. Meinhardt, A theory of biological pattern formation, Kybernetik, 12 (1972), 30-39. doi: 10.1007/BF00289234
![]() |
[3] | A. Gierer, H. Meinhardt, Biological pattern formation involving lateral inhibition, Lect. Math. Life. Sci., 7 (1974), 163-183. |
[4] |
Y. L. Song, R. Yang, G. Q. Sun, Pattern dynamics in a Gierer-Meinhardt model with a saturating term, Appl. Math. Model., 46 (2017), 476-491. doi: 10.1016/j.apm.2017.01.081
![]() |
[5] |
S. S. Chen, J. P. Shi, J. J. Wei, Bifurcation analysis of the Gierer-Meinhardt system with a saturation in the activator production, Appl. Anal., 93 (2014), 1115-1134. doi: 10.1080/00036811.2013.817559
![]() |
[6] |
R. C. Wu, Y. Zhou, Y. Shao, Bifurcation and Turing patterns of reaction-diffusion activator-inhibitor model, Physica A, 482 (2017), 597-610. doi: 10.1016/j.physa.2017.04.053
![]() |
[7] |
R. Yang, Y. L. Song, Spatial resonance and Turing-Hopf bifurcations in the Gierer-Meinhardt model, Nonlinear Anal.: RWA, 31 (2016), 356-387. doi: 10.1016/j.nonrwa.2016.02.006
![]() |
[8] |
S. G. Ruan, Diffusion-driven instability in the Gierer-Meinhardt model of morphogenesis, Nat. Res. Model., 11 (1998), 131-141. doi: 10.1111/j.1939-7445.1998.tb00304.x
![]() |
[9] | J. X. Liu, F. Q. Yi, J. J. Wei, Multiple bifurcation analysis and spatiotemporal patterns in a 1-D Gierer-Meinhardt model of morphogenesis, Int. J. Bifurcat. Chaos, 20 (2010), 1005-1025. |
[10] |
G. Q. Sun, C. H. Wang, Z. Y. Wu, Patterns dynamics of a Gierer-Meinhardt model with spatial effects, Nonlinear Dyn., 88 (2017), 1385-1396. doi: 10.1007/s11071-016-3317-9
![]() |
[11] |
S. S. Chen, J. P. Shi, Global attractivity of equilibrium in Gierer-Meinhardt system with activator production saturation and gene expression time delays, Nonlinear Anal.: RWA, 14 (2013), 1871-1886. doi: 10.1016/j.nonrwa.2012.12.004
![]() |
[12] |
R. Yang, Y. L. Song, Bifurcation analysis of a diffusive activator-inhibitor model in vascular mesenchymal cells, Int. J. Bifurcat. Chaos, 25 (2015), 1530026. doi: 10.1142/S0218127415300268
![]() |
[13] | J. Wei, M. Winter, On the Gierer-Meinhardt system with saturation, Commun. Contemp. Math., 8 (2004), 259-277. |
[14] |
S. S. Chen, J. P. Shi, J. J. Wei, Time delay-induced instability and hopf bifurcations in general reaction-diffusion systems, J. Nonlinear Sci., 23 (2013), 1-38. doi: 10.1007/s00332-012-9138-1
![]() |
[15] | S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer-Verlag New York, 2003. |
[16] | Y. J. Liu, Z. S. Li, X. M. Cai, Local stability and Hopf bifurcation analysis of the Arneodos system, Appl. Mech. Mater., 130 (2012), 2550-2557. |
[17] |
F. Q. Yi, J. Wei, J. P. Shi, Bifurcation and spatiotemporal patterns in a homogeneous diffusive predator-prey system, J. Differ. Equ., 246 (2009), 1944-1977. doi: 10.1016/j.jde.2008.10.024
![]() |
[18] |
M. X. Chen, R. C. Wu, B. Liu, L. P. Chen, Spatiotemporal dynamics in a ratio-dependent predator-prey model with time delay near the Turing-Hopf bifurcation point, Commun. Nonlinear Sci. Numer. Simul., 77 (2019), 141-167. doi: 10.1016/j.cnsns.2019.04.024
![]() |
[19] | L. Perko, Differential Equations and Dynamical Systems, Springer, NY, 1996. |
[20] |
J. C. Huang, Y. J. Gong, Multiple bifurcations in a predator-prey system of holling and leslie type with constant-yield prey harvesting, Int. J. Bifurcat. Chaos, 23 (2013), 1350164. doi: 10.1142/S0218127413501642
![]() |
[21] |
P. Yu, Computation of normal forms via a perturbation technique, J. Sound Vib., 211 (1998), 19-38. doi: 10.1006/jsvi.1997.1347
![]() |
[22] | Y. A. Kuznetsov, Elements of Applied Bifurcation Theory, Springer, New York, 1995. |
[23] |
H. Zhang, B. Niu, Dynamics in a plankton model with toxic substances and phytoplankton harvesting, Int. J. Bifurcat. Chaos, 30 (2020), 2050035. doi: 10.1142/S0218127420500352
![]() |
[24] | Y. Guo, B. Niu, Bautin bifurcation in delayed reaction-diffusion systems with application to the Segel-Jackson model, Discrete. Cont. Dyn. Syst. Ser. B, 24 (2018), 6005-6024. |
1. | Ming Wei, Shaopeng Zhang, Tao Liu, Bo Sun, The adjusted passenger transportation efficiency of nine airports in China with consideration of the impact of high-speed rail network development: A two-step DEA-OLS method, 2023, 109, 09696997, 102395, 10.1016/j.jairtraman.2023.102395 | |
2. | Zhen Wu, Po-Lin Lai, Fei Ma, Keun-Sik Park, Suthep Nimsai, Determining Spatial Relationships between Airports and Local Economy from Competitiveness Perspective: A Case Study of Airports in China, 2023, 10, 2226-4310, 138, 10.3390/aerospace10020138 | |
3. | Luigi dell’Olio, Andrés Rodríguez, Silvia Sipone, Modeling Airport Choice Using a Latent Class Logit Model, 2023, 10, 2226-4310, 703, 10.3390/aerospace10080703 | |
4. | Ming Wei, Yu Xiong, Bo Sun, Spatial effects of urban economic activities on airports’ passenger throughputs: A case study of thirteen cities and nine airports in the Beijing-Tianjin-Hebei region, China, 2025, 125, 09696997, 102765, 10.1016/j.jairtraman.2025.102765 | |
5. | Wolfgang Dupeyrat Luque, Chunyan Yu, Evolution of the Airport Industry and Regional Growth in the Pacific Alliance Member Countries, 2025, 127, 09696997, 102811, 10.1016/j.jairtraman.2025.102811 |