Article
Mathematics
Shangjiang Guo
Summary: This study investigates the existence, stability, and multiplicity of steady-state solutions and periodic solutions for a reaction-diffusion model with nonlocal delay effect and nonlinear boundary condition using Lyapunov-Schmidt reduction. It is found that when the interior reaction term is weaker than the boundary reaction term, there is no Hopf bifurcation, while if the interior reaction term is stronger, the existence of Hopf bifurcation depends on the interior reaction delay. The general results are illustrated by applying models with either a single delay or bistable boundary condition.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2021)
Article
Mathematics, Interdisciplinary Applications
Shangjiang Guo, Shangzhi Li, Bounsanong Sounvoravong
Summary: This paper investigates a reaction-diffusion model with delay effect and Dirichlet boundary condition, obtaining the existence and patterns of spatially nonhomogeneous steady-state solutions through Lyapunov-Schmidt reduction. Furthermore, the stability conditions of nontrivial synchronous steady-state solutions are discussed, along with the effect of time delay on pattern formation. The study also explores the spontaneous bifurcation of multiple branches of nonlinear wave solutions and their spatiotemporal patterns using symmetric bifurcation theory and representation theory of standard dihedral groups.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2021)
Article
Mathematical & Computational Biology
Yuting Ding, Gaoyang Liu, Yong An
Summary: In this paper, a tumor-immune system with diffusion and delays is investigated. The impact of delay on the stability of nonnegative equilibrium is analyzed, and the system undergoes Hopf bifurcation under certain critical delay values. The conditions for local asymptotic stability of nontrivial equilibria in a tumor-immune model with two delays are studied, and the diffusion of tumor cells can be restrained by controlling the associated time delays. Numerical simulations are provided to illustrate the analytical results.
MATHEMATICAL BIOSCIENCES AND ENGINEERING
(2022)
Article
Mathematics, Applied
Li Ma, Zhaosheng Feng
Summary: This paper investigates the dynamics of a class of two-species reaction-diffusion-advection competition models with time delay in a bounded domain, subject to homogeneous Dirichlet or no-flux boundary conditions. The study explores the existence of steady state solutions using the Lyapunov-Schmidt reduction method, and analyzes the stability and Hopf bifurcation at spatially nonhomogeneous steady states. Furthermore, the effect of advection on Hopf bifurcation is examined, revealing that an increase in convection rate makes the Hopf bifurcation phenomenon more likely to occur.
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2021)
Article
Mathematics
Yuanxian Hui, Yunfeng Liu, Zhong Zhao
Summary: This paper investigates a delayed reaction-diffusion equation with carrying capacity-driven diffusion. The stability of the positive equilibrium solutions and the existence of the Hopf bifurcation are considered by studying the principal eigenvalue of an associated elliptic operator. The properties of the bifurcating periodic solutions are obtained using the normal form theory and the center manifold reduction. Numerical simulations are provided to illustrate the main theoretical results.
Article
Mathematics, Interdisciplinary Applications
Jingjing Wang, Hongchan Zheng, Yunfeng Jia
Summary: This paper studies the effects of delay and diffusion on the dynamics of a bacteriaphages model. It is found that only diffusion cannot contribute to Turing instability, while delay or the combination of diffusion and delay can lead to Hopf bifurcation and patterns in the model. Numerical simulations are carried out to reveal these effects.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics, Applied
H. Y. Alfifi
Summary: This work explores stability and Hopf bifurcation analysis in a delayed diffusive logistic population equation in spatially heterogeneous environments. The Galerkin technique is used to consider solutions of the 1-D reaction-diffusion equation, with full maps of Hopf bifurcation determined for various parameters. The effects of free parameters on destabilizing or stabilizing solutions have been examined, with comparisons confirming the validity of the technique used.
APPLIED MATHEMATICS AND COMPUTATION
(2021)
Article
Mathematics, Applied
Hua Zhang, Hao Wang, Yongli Song, Junjie Wei
Summary: In this paper, a reaction-diffusion-advection model with memory-based diffusion and homogeneous Dirichlet boundary conditions is formulated. The existence of a nonconstant positive steady state is proven. The linear stability of the steady state is obtained by analyzing the eigenvalues of the associated linear operator, showing that the nonconstant steady state is always linearly stable regardless of the memory delay, while the model can also exhibit Hopf bifurcation as the memory delay varies. Moreover, theoretical and numerical results demonstrate that large advection eliminates oscillation patterns and drives species to concentrate downstream.
Article
Mathematics, Applied
Tingting Wen, Xiaoli Wang, Guohong Zhang
Summary: In this paper, the dynamics of a reaction-diffusion-advection equation with nonlocal delay effect and Dirichlet boundary condition are investigated. The existence of spatially nonhomogeneous steady states and the associated Hopf bifurcation are obtained by using the Lyapunov-Schmidt reduction. The theoretical results are also applied to models with a logistic growth rate and a weak Allee growth rate.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2023)
Article
Mathematics, Applied
Zhenzhen Li, Binxiang Dai
Summary: This paper investigates a classical two-species Lotka-Volterra competition-diffusion-advection model with time delay effect. It proves the existence of at least one spatially nonhomogeneous positive steady state and analyzes its local stability and Hopf bifurcation. The global stability of the positive steady state is also studied in the absence of time delay. The stability and direction of Hopf bifurcation are derived by introducing a weighted inner product associated with the advection rate, based on the idea of Chen et al (2018).
Article
Mathematics
Hongying Shu, Wanxiao Xu, Xiang-Sheng Wang, Jianhong Wu
Summary: We formulate and analyze a general reaction-diffusion equation with delay, inspired by age-structured spruce budworm population dynamics with spatial diffusion by matured individuals. The model exhibits bistability due to nonlinear birth function and predation by birds. We establish results on the stability and global Hopf bifurcation from the spatially homogeneous steady state with maturation delay as a bifurcation parameter. We also use degree theory to determine the diffusion rate intervals for spatially heterogeneous steady states. Numerical experiments demonstrate interesting spatial-temporal patterns.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2022)
Article
Mathematics, Applied
Xiuli Sun, Rong Yuan
Summary: This paper investigates the dynamics of a general nonlocal delayed reaction-diffusion equations with Dirichlet boundary condition. The stability and bifurcation of spatially nonhomogeneous steady-state solutions, as well as the existence of Hopf bifurcations with time delay, are analyzed. Numerical simulations are conducted to illustrate the theoretical results.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2022)
Article
Mathematics
Ruizhi Yang, Xiao Zhao, Yong An
Summary: In this study, a delayed predator-prey model with diffusion and anti-predator behavior is investigated. The stability of the positive equilibrium is analyzed, and the existence of Hopf bifurcation is discussed based on the Hopf bifurcation theory. The properties of Hopf bifurcation are derived using the theory of center manifold and normal form method. Finally, the impact of time delay on the model is examined through numerical simulations.
Article
Mathematics, Applied
Wen Wang, Shutang Liu
Summary: This paper presents the Turing-Hopf bifurcation analysis and resulting spatiotemporal dynamics in a single-species reaction-diffusion model with nonlocal delay. Linear stability analysis is used to determine the conditions for Turing-Hopf bifurcation, and weakly nonlinear analysis is employed to derive the amplitude equations for the slow-time evolution of critical modes. The use of amplitude equations allows for the determination of stability conditions and prediction of spatiotemporal patterns near the bifurcation point. Numerical simulations are conducted to verify the theoretical results.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2023)
Article
Mathematics, Applied
Li Ma, Dan Wei
Summary: The article focuses on the Hopf bifurcation of a delayed reaction-diffusion equation with advection term, showing the existence of spatially non-homogeneous steady-state solutions and elucidating the effect of advection on Hopf bifurcation values.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2021)
Article
Engineering, Mechanical
Qingyan Shi, Yongli Song
NONLINEAR DYNAMICS
(2016)
Article
Mathematics, Applied
Yongli Song, Tonghua Zhang, Yahong Peng
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2016)
Article
Mathematics, Interdisciplinary Applications
Heping Jiang, Jiao Jiang, Yongli Song
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2016)
Article
Mathematics, Interdisciplinary Applications
Xin Cao, Yongli Song, Tonghua Zhang
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2016)
Article
Mathematics, Interdisciplinary Applications
Jiao Jiang, Yongli Song, Pei Yu
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2016)
Article
Mathematics, Applied
Rui Yang, Yongli Song
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2016)
Article
Engineering, Mechanical
Xiaosong Tang, Yongli Song, Tonghua Zhang
NONLINEAR DYNAMICS
(2016)
Article
Mathematics
Yongli Song, Shuhao Wu, Hao Wang
JOURNAL OF DIFFERENTIAL EQUATIONS
(2019)
Article
Mathematics, Applied
Shuhao Wu, Yongli Song
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2019)
Article
Mathematics, Interdisciplinary Applications
Danxia Song, Yongli Song, Chao Li
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2020)
Article
Mathematics, Applied
Danxia Song, Chao Li, Yongli Song
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2020)
Article
Mathematics, Applied
Yongli Song, Gaoxiang Yang
APPLIED MATHEMATICS LETTERS
(2020)
Article
Mathematics, Applied
Shuhao Wu, Yongli Song
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2020)
Article
Mathematics
Yongli Song, Yahong Peng, Tonghua Zhang
Summary: This paper presents an effective algorithm for computing the normal forms of Hopf bifurcations in memory-based diffusion systems, using a diffusive predator-prey system as a case study. The research demonstrates the direction and stability of delay-induced Hopf bifurcations and confirms the existence of stable spatially inhomogeneous periodic solutions with mode-1 and mode-2 spatial patterns through numerical simulations.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2021)
Article
Mathematics, Applied
Qingyan Shi, Junping Shi, Yongli Song
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
(2019)
Article
Mathematics, Applied
Geunsu Choi, Mingu Jung, Sun Kwang Kim, Miguel Martin
Summary: This paper studies weak-star quasi norm attaining operators and proves that the set of such operators is dense in the space of bounded linear operators regardless of the choice of Banach spaces. It is also shown that weak-star quasi norm attaining operators have distinct properties from other types of norm attaining operators, although they may share some equivalent properties under certain conditions.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Maria Lorente, Francisco J. Martin-Reyes, Israel P. Rivera-Rios
Summary: In this paper, we provide quantitative one-sided estimates that recover the dependences in the classical setting. We estimate the one-sided maximal function in Lorentz spaces and demonstrate the applicability of the conjugation method for commutators in this context.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Fernando Cobos, Luz M. Fernandez-Cabrera
Summary: We provide a necessary and sufficient condition for the weak compactness of bilinear operators interpolated using the real method. However, this characterization does not hold for interpolated operators using the complex method.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Ovgue Gurel Yilmaz, Sofiya Ostrovska, Mehmet Turan
Summary: The Lupas q-analogue Rn,q, the first q-version of the Bernstein polynomials, was originally proposed by A. Lupas in 1987 but gained popularity 20 years later when q-analogues of classical operators in approximation theory became a focus of intensive research. This work investigates the continuity of operators Rn,q with respect to the parameter q in both the strong operator topology and the uniform operator topology, considering both fixed and infinite n.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
M. Agranovsky, A. Koldobsky, D. Ryabogin, V. Yaskin
Summary: This article modifies the concept of polynomial integrability for even dimensions and proves that ellipsoids are the only convex infinitely smooth bodies satisfying this property.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Abel Komalovics, Lajos Molnar
Summary: In this paper, a parametric family of two-variable maps on positive cones of C*-algebras is defined and studied from various perspectives. The square roots of the values of these maps under a faithful tracial positive linear functional are considered as a family of potential distance measures. The study explores the problem of well-definedness and whether these distance measures are true metrics, and also provides some related trace characterizations. Several difficult open questions are formulated.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Frederic Bayart
Summary: The passage describes the construction of an operator on a separable Hilbert space that is 5-hypercyclic for all δ in the range (ε, 1) and is not 5-hypercyclic for all δ in the range (0, ε).
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Helene Frankowska, Nikolai P. Osmolovskii
Summary: This paper investigates second-order optimality conditions for the minimization problem of a C2 function f on a general set K in a Banach space X. Both necessary and sufficient conditions are discussed, with the sufficiency condition requiring additional assumptions. The paper demonstrates the validity of these assumptions for the case when the set K is an intersection of sets described by smooth inequalities and equalities, such as in mathematical programming problems. The novelty of the approach lies in the arbitrary nature of the set K and the straightforward proofs.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Ole Fredrik Brevig, Kristian Seip
Summary: This paper studies the Hankel operator on the Hardy space and discusses its minimal and maximal norms, as well as the relationship between the maximal norm and the properties of the function.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Alexander Meskhi
Summary: Rubio de Francia's extrapolation theorem is established for new weighted grand Morrey spaces Mp),lambda,theta w (X) with weights w beyond the Muckenhoupt Ap classes. This result implies the one-weight inequality for operators of Harmonic Analysis in these spaces for appropriate weights. The necessary conditions for the boundedness of the Hardy-Littlewood maximal operator and the Hilbert transform in these spaces are also obtained. Some structural properties of new weighted grand Morrey spaces are investigated. Problems are studied in the case when operators and spaces are defined on spaces of homogeneous type.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Maud Szusterman
Summary: In this work, the necessary conditions on the structure of the boundary of a convex body K to satisfy all inequalities are investigated. A new solution for the 3-dimensional case is obtained in particular.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Rami Ayoush, Michal Wojciechowski
Summary: In this article, lower bounds for the lower Hausdorff dimension of finite measures are provided under certain restrictions on their quaternionic spherical harmonics expansions. This estimate is analogous to a result previously obtained by the authors for complex spheres.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
F. G. Abdullayev, V. V. Savchuk
Summary: This paper investigates the convergence and theorem proof of the Takenaka-Malmquist system and Fejer-type operator on the unit circle, and provides relevant results on the class of holomorphic functions representable by Cauchy-type integrals with bounded densities.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Sofiya Ostrovska, Mikhail I. Ostrovskii
Summary: This work aims to establish new results on the structure of transportation cost spaces. The main outcome of this paper states that if a metric space X contains an isometric copy of L1 in its transportation cost space, then it also contains a 1-complemented isometric copy of $1.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Pilar Rueda, Enrique A. Sanchez Perez
Summary: We prove a factorization theorem for Lipschitz operators acting on certain subsets of metric spaces of measurable functions and with values on general metric spaces. Our results show how a Lipschitz operator can be extended to a subset of other metric space of measurable functions that satisfies the following optimality condition: it is the biggest metric space, formed by measurable functions, to which the operator can be extended preserving the Lipschitz constant. Also, we demonstrate the coarsest metric that can be given for a metric space in which an order bounded lattice-valued-Lipschitz map is defined, and provide concrete examples involving the relevant space L0(mu).
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)