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

international Journal of Biomathematics 2024年第8期17卷 309-347页

作者： Qi An Xingyu Guo Xuebing Zhang College of Mathematics and Statistics Nanjing University of Information Science and Technology Nanjing 210044 P.R.China 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

This is an Open Access article published by World Scientific Publishing *** 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 *** cognitive abilities of animals,such as memory,have a significant impact on their movement in *** this paper,we consider a radio-dependent model with memorybased diffusion under the conditions of Neumann *** stability of a positive equilibrium and the existence of the Turing-Hopf bifurcation induced by memory diffusion and memory delay are carried out in ***,our findings indicate that with a relatively short average memory period,the large memory diffusion can stabilize an otherwise unstable *** 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 *** coefficients within the normal form are systematically determined through matrix operations,and these results can also be applied to other models with memory ***,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

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The Optimal Closed-Form Linear Canonical Wigner Distribution 6

The Optimal Closed-Form Linear Canonical Wigner Distribution

引用

6th international Conference on Information Communication and Signal Processing, ICICSP 2023

作者： Zhang, Zhichao School of Mathematics and Statistics Center for Applied Mathematics of Jiangsu Province Nanjing University of Information Science and Technology Jiangsu International Joint Laboratory on System Modeling and Data Analysis Nanjing China

ISBN: (纸本)9798350339994

This study devotes to Heisenberg's uncertainty inequalities under the closed-form instantaneous cross-correlation function Wigner distribution (CICFWD), whose generalizability enables it to be a representative Wigner distribution (WD) in the linear canonical transform (LCT) domain. A relation between the spread in the time-CICFWD domain and the spreads and moments in LCT domains is established. We then obtain two versions of lower bounds on the uncertainty product of spreads in time-CICFWD and LCT-CICFWD domains. The first is the tightest universal lower bound for all signals, and the other is a lower bound for complex-valued signals. As a result, uncertainty principles for the traditional WD are revisited. The optimal LCT free parameters selection problems of the CICFWD are also well-addressed from the perspectives of the highest time-frequency resolution and its best estimation accuracy, respectively. © 2023 IEEE.

关键词： linear canonical Wigner distribution lower bound time-frequency resolution uncertainty principle

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Qualitative analysis of a Diffusive Predator-prey Model with Nonlcoal Fear Effect

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数学理论与应用 2024年第3期44卷 67-82页

作者： Shen Zhongyuan Zhang Xuebing Li Shunjie Center for Applied Mathematics of Jiangsu Province Jiangsu International Joint Laboratory on System Modeling and Data AnalysisNanjing 210044China

In this paper,we establish a delayed predator-prey model with nonlocal fear ***,the existence,uniqueness,and persistence of solutions of the model are ***,the local stability,Turing bifurcation,and Hopf bifurcation of the constant equilibrium state are analyzed by examining the characteristic *** global asymptotic stability of the positive equilibrium point is investigated using the Lyapunov function ***,the correctness of the theoretical analysis results is verified through numerical simulations.

关键词： Delay Nonlocal fear effect Global stability Hopf bifurcation

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Strong Time-Periodic Solutions to the 3d Oceanic Primitive Equations with the Gent-Mcwilliams-Redi Eddy Parametrization Model and Arbitrary Large Outer Forces

SSRN

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SSRN 2025年

作者： Zhang, Jie Liu, Wenjun School of Mathematics and Statistics Nanjing University of Information Science and Technology Nanjing210044 China Jiangsu International Joint Laboratory on System Modeling and Data Analysis Center for Applied Mathematics of Jiangsu Province Nanjing University of Information Science and Technology Nanjing210044 China

To capture the effect of mesoscale eddies on oceanic temperature and salinity, we take the Gent-McWilliams-Redi eddy parametrization model into account in an ocean model with outer forces consisting of the 3D primitive equations and a set of advection-diffusion equations describing the oceanic tracers of temperature and salinity. The existence of strong time-periodic ($T$-periodic) solutions for this model is established under three time-periodic outer forces without any smallness conditions, provided that the density function for pressure, temperature and salinity satisfies the certain regularity assumption. Firstly, we prove the existence of a weak $T$-periodic solution relying on the Faedo-Galerkin method, Brouwer's fixed-point theorem and a priori bounds. Secondly, we prove the global well-posedness of strong solutions for arbitrary large outer forces and initial data that are in appropriately chosen function classes. Finally, we adopt the method of the weak-strong uniqueness to obtain a strong $T$-periodic solution for this model. © 2025, The Authors. All rights reserved.

关键词： Fixed point arithmetic

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Convolution Type of Metaplectic Cohen’s Distribution Time-Frequency analysis Theory, Method and Technology

arXiv

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arXiv 2024年

作者： Cui, Manjun Zhang, Zhichao Han, Jie Chen, Yunjie Cao, Chunzheng The School of Mathematics and Statistics The Center for Applied Mathematics of Jiangsu Province The Jiangsu International Joint Laboratory on System Modeling and Data Analysis Nanjing University of Information Science and Technology Nanjing210044 China The School of Remote Sensing and Geomatics Engineering Nanjing University of Information Science and Technology Nanjing210044 China

The conventional Cohen’s distribution can’t meet the requirement of additive noises jamming signals high-performance denoising under the condition of low signal-to-noise ratio, it is necessary to integrate the metaplectic transform for non-stationary signal fractional domain time-frequency analysis. In this paper, we blend time-frequency operators and coordinate operator fractionizations to formulate the definition of the metaplectic Wigner distribution, based on which we integrate the generalized metaplectic convolution to address the unified representation issue of the convolution type of metaplectic Cohen’s distribution (CMCD), whose special cases and essential properties are also derived. We blend Wiener filter principle and fractional domain filter mechanism of the metaplectic transform to design the least-squares adaptive filter method in the metaplectic Wigner distribution domain, giving birth to the least-squares adaptive filter-based CMCD whose kernel function can be adjusted with the input signal automatically to achieve the minimum mean-square error (MSE) denoising in Wigner distribution domain. We discuss the optimal symplectic matrices selection strategy of the proposed adaptive CMCD through the minimum MSE minimization modeling and solving. Some examples are also carried out to demonstrate that the proposed filtering method outperforms some state-of-the-arts including Wiener filter and fixed kernel functions-based or adaptive Cohen’s distribution in noise suppression. Copyright © 2024, The Authors. All rights reserved.

关键词： Adaptive filters

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Mathematical modeling and analysis of atherosclerosis based on fluid-multilayered poroelastic structure interaction model

Research Square

引用

Research Square 2023年

作者： An, Yanning Liu, Wenjun School of Mathematics and Statistics Nanjing University of Information Science and Technology Nanjing210044 China Jiangsu International Joint Laboratory on System Modeling and Data Analysis Center for Applied Mathematics of Jiangsu Province Nanjing University of Information Science and Technology Nanjing210044 China

In this paper, we establish a new model of atherosclerosis in the early stage based on fluid-structure interaction (FSI) model of blood vessel and prove the existence of weak solutions. The model consists of Navier-Stokes equation, Biot equations, and reaction-diffusion equations, which involves the effect of blood flow velocity on the concentration of low density lipoprotein (LDL) and other biological components. We first divide the new model into a FSI submodel and a coupled reaction-diffusion submodel, respectively. Then, by using Rothe’s method and operator splitting numerical scheme, we obtain the existence of weak solution of FSI submodel. In order to solve the nonlinear term representing the consumption of oxidized low density lipoprotein (oxLDL), we construct a regular system. The results in FSI submodel together with Schauder’s fixed point theorem allow us to obtain the existence of non-negative weak solutions for the reaction-diffusion submodel by showing the existence and non-negativity of weak solutions for the regular system. © 2023, CC BY.

关键词： Navier Stokes equations

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Continuous data assimilation for the three dimensional primitive equations with magnetic field

arXiv

引用

arXiv 2023年

作者： Zhao, Yongqing Liu, Wenjun Lv, Guangying Wang, Yuepeng School of Mathematics and Statistics Nanjing University of Information Science and Technology Nanjing210044 China Jiangsu International Joint Laboratory on System Modeling and Data Analysis Center for Applied Mathematics of Jiangsu Province Nanjing University of Information Science and Technology Nanjing210044 China

In this paper, the problem of continuous data assimilation of three dimensional primitive equations with magnetic field in thin domain is studied. We establish the well-posedness of the assimilation system and prove that the H2-strong solution of the assimilation system converges exponentially to the reference solution in the sense of L2 as t → ∞. We also study the sensitivity analysis of the assimilation system and prove that a sequence of solutions of the difference quotient equation converge to the unique solution of the formal sensitivity *** Codes 35Q35, 34D06, 37C50 Copyright © 2023, The Authors. All rights reserved.

关键词： Sensitivity analysis

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The horizontal magnetic primitive equations approximation of the anisotropic MHD equations in a thin 3D domain

arXiv

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arXiv 2023年

In this paper, we give a rigorous justification of the deviation of the primitive equations with only horizontal viscosity and magnetic diffusivity (PEHM) as the small aspect ratio limit of the incompressible three-dimensional scaled horizontal viscous MHD (SHMHD) equations. Choosing an aspect ratio parameter Ε ∈ (0, ∞), we consider the case that if the horizontal and vertical viscous coefficients are of µ = O(1) and ν = O(Εα), and the orders of magnetic diffusion coefficients k and σ are k = O(1) and σ = O(Εα), with α > 2, then the limiting system is the PEHM as Ε goes to zero. For H1-initial data, we prove that the global weak solutions of the SHMHD equations converge strongly to the local-in-time strong solutions of the PEHM, as Ε tends to zero. For H1-initial data with additional regularity (∂zÃ0, ∂zB˜0) ∈ Lp(Ω)(2 2-initial data, we show that the local-in-time strong solutions of the SHMHD equations converge strongly to the global-in-time strong solutions of the PEHM, as Ε goes to zero. Moreover, the rate of convergence is of the order O(Εγ/2), where γ = min{2, α − 2} with α ∈ (2, ∞). It should be noted that in contrast to the case α > 2, the case α = 2 has been investigated by Du and Li in [14], in which they consider the PEM and the rate of global-in-time convergences is of the order O(Ε).MSC Codes 35Q30, 76D03, 76D05, 35Q86, 76W05 Copyright © 2023, The Authors. All rights reserved.

关键词： Aspect ratio

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Multi-dimensional Graph Linear Canonical Transform

arXiv

引用

arXiv 2024年

作者： Li, Na Zhang, Zhichao Han, Jie Chen, Yunjie Cao, Chunzheng School of Mathematics and Statistics Center for Applied Mathematics of Jiangsu Province Jiangsu International Joint Laboratory on System Modeling and Data Analysis Nanjing University of Information Science and Technology Nanjing210044 China Key Laboratory of System Control and Information Processing Ministry of Education Shanghai200240 China Key Laboratory of Computational Science and Application of Hainan Province Haikou571158 China School of Remote Sensing and Geomatics Engineering Nanjing University of Information Science and Technology Nanjing210044 China

Many multi-dimensional (M-D) graph signals appear in the real world, such as digital images, sensor network measurements and temperature records from weather observation stations. It is a key challenge to design a transform method for processing these graph M-D signals in the linear canonical transform domain. This paper proposes the two-dimensional graph linear canonical transform based on the central discrete dilated Hermite function (2-D CDDHFs-GLCT) and the two-dimensional graph linear canonical transform based on chirp multiplication-chirp convolution-chirp multiplication decomposition (2-D CM-CC-CM-GLCT). Then, extending 2-D CDDHFs-GLCT and 2-D CM-CC-CM-GLCT to M-D CDDHFs-GLCT and M-D CM-CC-CM-GLCT. In terms of the computational complexity, additivity and reversibility, M-D CDDHFs-GLCT and M-D CM-CC-CM-GLCT are compared. Theoretical analysis shows that the computational complexity of M-D CM-CC-CM-GLCT algorithm is obviously reduced. Simulation results indicate that M-D CM-CC-CM-GLCT achieves comparable additivity to M-D CDDHFs-GLCT, while M-D CM-CC-CM-GLCT exhibits better reversibility. Finally, M-D GLCT is applied to data compression to show its application advantages. The experimental results reflect the superiority of M-D GLCT in the algorithm design and implementation of data compression. Copyright © 2024, The Authors. All rights reserved.

关键词： Chirp modulation

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Graph Chirp Signal and Graph Fractional Vertex-Frequency Energy Distribution

arXiv

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arXiv 2025年

作者： Cui, Manjun Zhang, Zhichao School of Mathematics and Statistics The Center for Applied Mathematics of Jiangsu Province The Jiangsu International Joint Laboratory on System Modeling and Data Analysis Nanjing University of Information Science and Technology Nanjing210044 China School of Mathematics and Statistics Nanjing University of Information Science and Technology Nanjing210044 China Key Laboratory of System Control and Information Processing Ministry of Education Shanghai Jiao Tong University Shanghai200240 China Key Laboratory of Computational Science and Application of Hainan Province Hainan Normal University Haikou571158 China

Graph signal processing (GSP) has emerged as a powerful framework for analyzing data on irregular domains. In recent years, many classical techniques in signal processing (SP) have been successfully extended to GSP. Among them, chirp signals play a crucial role in various SP applications. However, graph chirp signals have not been formally defined despite their importance. Here, we define graph chirp signals and establish a comprehensive theoretical framework for their analysis. We propose the graph fractional vertex-frequency energy distribution (GFED), which provides a powerful tool for processing and analyzing graph chirp signals. We introduce the general fractional graph distribution (GFGD), a generalized vertex-frequency distribution, and the reduced interference GFED, which can suppress cross-term interference and enhance signal clarity. Furthermore, we propose a novel method for detecting graph signals through GFED domain filtering, facilitating robust detection and analysis of graph chirp signals in noisy environments. Moreover, this method can be applied to real-world data for denoising more effective than some state-of-the-arts, further demonstrating its practical significance. Copyright © 2025, The Authors. All rights reserved.

关键词： Wiener filtering

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