Bifurcation analysis of a diffusive radio-dependent model with spatial memory  

作　　者：Qi An Xingyu Guo Xuebing Zhang 

机构地区：[1]College of Mathematics and Statistics Nanjing University of Information Science and Technology Nanjing 210044,P.R.China [2]Jiangsu International Joint Laboratory on System Modeling and Data Analysis Center for Applied Mathematics of Jiangsu Province Nanjing University of Information Science and Technology Nanjing 210044,P.R.China

出　　处：《International Journal of Biomathematics》2024年第8期309-347,共39页生物数学学报(英文版)

基　　金：supported by National Natural Science Foundation of China 12101318;Natural Science Found of Jiangsu Province BK20200805 and Natural Science Fund Project of Colleges in Jiangsu Province 20KJB110009.

摘　　要：This is an Open Access article published by World Scientific Publishing Company.It is distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0(CC BY-NC-ND)License,which permits use,distribution and reproduction,provided that the original work is properly cited,the use is non-commercial and no modifications or adaptations are made.The cognitive abilities of animals,such as memory,have a significant impact on their movement in space.In this paper,we consider a radio-dependent model with memorybased diffusion under the conditions of Neumann boundary.The stability of a positive equilibrium and the existence of the Turing-Hopf bifurcation induced by memory diffusion and memory delay are carried out in details.Notably,our findings indicate that with a relatively short average memory period,the large memory diffusion can stabilize an otherwise unstable equilibrium.In addition,the third-order truncated normal form for the Turing-Hopf bifurcation restricted to the central manifold is derived,which can reveal the generation of some steady-state and time-periodic solutions with spatial heterogeneity.The coefficients within the normal form are systematically determined through matrix operations,and these results can also be applied to other models with memory diffusion.Ultimately,leveraging the theoretical findings,we elucidated the intricate spatial-temporal dynamics and their associated parameter scopes caused by Turing-Hopf bifurcation through numerical simulations.

关 键 词：Spatial memory normal form Turing-Hopf bifurcation spatio-temporal patterns periodic solutions 

分 类 号：O175[理学—数学]