Article
Mathematics
Qing Li, Junfeng He
Summary: This paper focuses on a ratio-dependent predator-prey model with cross-diffusion of quasilinear fractional type. By using the theory of local bifurcation, it is proven that there exists a positive non-constant steady state originating from the semi-trivial solution of this problem. Furthermore, based on spectral analysis, this bifurcating steady state is shown to be asymptotically stable when the cross diffusion rate approaches a critical value. Finally, numerical simulations and ecological interpretations are presented in the discussion section.
ELECTRONIC RESEARCH ARCHIVE
(2023)
Article
Engineering, Mechanical
Xuebing Zhang, Qi An, Ling Wang
Summary: In this study, a delayed diffusive predator-prey model with fear effect is considered due to the delay in the impact of fear on the growth rate of prey. The existence of equilibria, occurrence of Turing, Hopf and Turing-Hopf bifurcation, and global asymptotic stability of the positive equilibrium are analyzed, with various spatiotemporal patterns induced by delay confirmed through numerical simulations.
NONLINEAR DYNAMICS
(2021)
Article
Mathematics, Applied
Wonhyung Choi, Kwangjoong Kim, Inkyung Ahn
Summary: This article explores a predator-prey system in which the diffusion of predators is influenced by a certain type of prey-dependent diffusion. The source of prey population depends on the location within a bounded domain habitat with spatial heterogeneity. The study reveals that predators can invade a habitat region through prey-dependent diffusion and investigates the existence and uniqueness of a positive steady state using the fixed point index theory in a positive cone in a Banach space. The coexistence state is found to be unique under certain conditions related to prey diffusion rate and the average of the prey's resource function.(c) 2023 Elsevier Inc. All rights reserved.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2023)
Article
Mathematics, Applied
Shuyan Qiu, Chunlai Mu, Xinyu Tu
Summary: This work presents a mathematical model that studies the dynamics of two predators and one prey, considering the signal-dependent diffusion and sensitivity, under homogeneous Neumann boundary conditions. The study proves the existence and boundedness of positive classical solutions in any dimensions, using L-p-estimate techniques. The asymptotic behavior of solutions to a specific model, with Lotka-Volterra type functional responses and density-dependent death rates for the predators and logistic type for the prey, is also established.
JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS
(2023)
Article
Mathematics, Applied
Claudio Arancibia-Ibarra, Pablo Aguirre, Jose Flores, Peter van Heijster
Summary: The study investigates the Bazykin predator-prey model and confirms the existence and stability of two interior equilibrium points. Various bifurcations, such as saddle-node bifurcations, Hopf bifurcations, etc., are shown in the model. Numerical simulations reveal the impact of changing predator consumption rate and conversion efficiency on the basin of attraction of stable equilibrium points.
APPLIED MATHEMATICS AND COMPUTATION
(2021)
Article
Mathematics, Applied
Jia Liu, Yun Kang
Summary: This paper discusses a diffusive predator-prey model with fear effect. By mathematical and numerical analyses, the author finds that fear can prevent the occurrence of limit cycle oscillation and increase the stability of the system, while diffusion can induce chaos in the system.
NONLINEAR ANALYSIS-MODELLING AND CONTROL
(2022)
Article
Mathematics, Interdisciplinary Applications
Caiyun Wang, Jing Li, Ruiqiang He
Summary: The study shows that the frequency diffusion of prey leads to a sparse density of predators. Increasing the conversion rate into predator biomass may induce pattern transitions of the predator, from a spotted pattern to a black-eye pattern, with an intermediate state of a mixture of spot and stripe patterns. The simulation results and analysis demonstrate that the diffusion rate and the intrinsic factor mutually influence the persistence of the predator-prey system.
Article
Mathematical & Computational Biology
Pan Zheng
Summary: This paper deals with a two-species competitive predator-prey system with density-dependent diffusion, and rigorously proves the global boundedness of the model. Moreover, in some particular cases, the asymptotic stabilization and precise convergence rates of globally bounded solutions are established.
MATHEMATICAL BIOSCIENCES AND ENGINEERING
(2022)
Article
Engineering, Mechanical
Zhihui Wang, Yuanshi Wang
Summary: This paper examines the impact of species' diffusion and environmental heterogeneity on population dynamics through a mathematical model, demonstrating how different diffusion rates can affect species interaction outcomes and how the population abundance of a diffusing prey can exceed that of a non-diffusing prey.
NONLINEAR DYNAMICS
(2021)
Article
Mathematics, Applied
Ailing Xiang, Liangchen Wang
Summary: This paper investigates the predator-prey system with density-dependent motilities and indirect pursuit-evasion interaction. Under certain assumptions, the global existence and boundedness of classical solutions are proven in two dimensions, and it is also shown that the global solutions are uniformly bounded with respect to time in higher dimensions.
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2023)
Article
Mathematics, Applied
Leoncio Q. Rodriguez, Jia Zhao, Luis F. Gordillo
Summary: A spatial Rosenzweig-MacArthur model was studied under certain assumptions, showing the existence of positive solutions at the steady state through bifurcation analysis. Results indicate that models with linear and nonlinear diffusion for prey have similar positive solution curves near the bifurcation point, but diverge significantly as the bifurcation parameter approaches zero.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2021)
Article
Mathematics, Applied
Xin Zhao, Zhijun Zeng
Summary: This paper analyzes the features of a stochastically perturbed two-species predator-prey patch-system with ratio-dependent functional response. It proves that the system has a unique global positive solution and presents sufficient criteria for the existence and uniqueness of an ergodic stationary distribution of positive solutions to the system by establishing a series of suitable Lyapunov functions.
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS
(2022)
Article
Mathematics, Applied
Yongli Cai, Qian Cao, Zhi-An Wang
Summary: This paper investigates the global dynamics of a ratio-dependent predator-prey system with prey-taxis. By establishing a mathematical model and conducting numerical simulations, we find that pattern formation may occur and prey-taxis drives the evolution of spatial inhomogeneity.
APPLICABLE ANALYSIS
(2022)
Article
Mathematics, Applied
Duo Zhang, Xuegang Hu
Summary: This paper investigates the global boundedness and asymptotic stability of the solution of the two-predator and one-prey systems with density-dependent motion in a n-dimensional bounded domain with Neumann boundary conditions. The previous paper by Qiu et al. (J Dyn Differ Equ, 1-25, 2021) proved the global existence and uniform boundedness of classical solution by limiting the conditions on motility functions and the coefficients of logistic source. In contrast, this paper relaxes the limitation conditions in Qiu et al. (2021) by constructing the weight function. Moreover, the global stabilities of nonnegative spatially homogeneous equilibria for the special model are established.
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
(2023)
Article
Mathematics, Applied
Qian Cao, Yongli Cai, Yong Luo
Summary: Using bifurcation theory, this study investigates the local and global structures of steady states in a ratio-dependent predator-prey system with prey-taxis. The stability criteria for these bifurcating steady states are determined through asymptotic analysis and eigenvalue perturbation. Numerical simulations are utilized to illustrate pattern formation.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
(2022)
Article
Mathematics, Applied
Peter Frolkovic, Nikola Gajdosova
Summary: This paper presents compact semi-implicit finite difference schemes for solving advection problems using level set methods. Through numerical tests and stability analysis, the accuracy and stability of the proposed schemes are verified.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Md. Rajib Arefin, Jun Tanimoto
Summary: Human behaviors are strongly influenced by social norms, and this study shows that injunctive social norms can lead to bi-stability in evolutionary games. Different games exhibit different outcomes, with some showing the possibility of coexistence or a stable equilibrium.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Dingyi Du, Chunhong Fu, Qingxiang Xu
Summary: A correction and improvement are made on a recent joint work by the second and third authors. An optimal perturbation bound is also clarified for certain 2 x 2 Hermitian matrices.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Pingrui Zhang, Xiaoyun Jiang, Junqing Jia
Summary: In this study, improved uniform error bounds are developed for the long-time dynamics of the nonlinear space fractional Dirac equation in two dimensions. The equation is discretized in time using the Strang splitting method and in space using the Fourier pseudospectral method. The major local truncation error of the numerical methods is established, and improved uniform error estimates are rigorously demonstrated for the semi-discrete scheme and full-discretization. Numerical investigations are presented to verify the error bounds and illustrate the long-time dynamical behaviors of the equation with honeycomb lattice potentials.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Kuan Zou, Wenchen Han, Lan Zhang, Changwei Huang
Summary: This research extends the spatial PGG on hypergraphs and allows cooperators to allocate investments unevenly. The results show that allocating more resources to profitable groups can effectively promote cooperation. Additionally, a moderate negative value of investment preference leads to the lowest level of cooperation.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Kui Du
Summary: This article introduces two new regularized randomized iterative algorithms for finding solutions with certain structures of a linear system ABx = b. Compared to other randomized iterative algorithms, these new algorithms can find sparse solutions and have better performance.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Shadi Malek Bagomghaleh, Saeed Pishbin, Gholamhossein Gholami
Summary: This study combines the concept of vanishing delay arguments with a linear system of integral-algebraic equations (IAEs) for the first time. The piecewise collocation scheme is used to numerically solve the Hessenberg type IAEs system with vanishing delays. Well-established results regarding regularity, existence, uniqueness, and convergence of the solution are presented. Two test problems are studied to verify the theoretical achievements in practice.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Qi Hu, Tao Jin, Yulian Jiang, Xingwen Liu
Summary: Public supervision plays an important role in guiding and influencing individual behavior. This study proposes a reputation incentives mechanism with public supervision, where each player has the authority to evaluate others. Numerical simulations show that reputation provides positive incentives for cooperation.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Werner M. Seiler, Matthias Seiss
Summary: This article proposes a geometric approach for the numerical integration of (systems of) quasi-linear differential equations with singular initial and boundary value problems. It transforms the original problem into computing the unstable manifold at a stationary point of an associated vector field, allowing efficient and robust solutions. Additionally, the shooting method is employed for boundary value problems. Examples of (generalized) Lane-Emden equations and the Thomas-Fermi equation are discussed.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Lisandro A. Raviola, Mariano F. De Leo
Summary: We evaluated the performance of novel numerical methods for solving one-dimensional nonlinear fractional dispersive and dissipative evolution equations and showed that the proposed methods are effective in terms of accuracy and computational cost. They can be applied to both irreversible models and dissipative solitons, offering a promising alternative for solving a wide range of evolutionary partial differential equations.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Yong Wang, Jie Zhong, Qinyao Pan, Ning Li
Summary: This paper studies the set stability of Boolean networks using the semi-tensor product of matrices. It introduces an index-vector and an algorithm to verify and achieve set stability, and proposes a hybrid pinning control technique to reduce computational complexity. The issue of synchronization is also discussed, and simulations are presented to demonstrate the effectiveness of the results obtained.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Ling Cheng, Sirui Zhang, Yingchun Wang
Summary: This paper considers the optimal capacity allocation problem of integrated energy systems (IESs) with power-gas systems for clean energy consumption. It establishes power-gas network models with equality and inequality constraints, and designs a novel full distributed cooperative optimal regulation scheme to tackle this problem. A distributed projection operator is developed to handle the inequality constraints in IESs. The simulation demonstrates the effectiveness of the distributed optimization approach.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Abdurrahim Toktas, Ugur Erkan, Suo Gao, Chanil Pak
Summary: This study proposes a novel image encryption scheme based on the Bessel map, which ensures the security and randomness of the ciphered images through the chaotic characteristics and complexity of the Bessel map.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Xinjie Fu, Jinrong Wang
Summary: In this paper, we establish an SAIQR epidemic network model and explore the global stability of the disease in both disease-free and endemic equilibria. We also consider the control of epidemic transmission through non-instantaneous impulsive vaccination and demonstrate the sustainability of the model. Finally, we validate the results through numerical simulations using a scale-free network.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Maria Han Veiga, Lorenzo Micalizzi, Davide Torlo
Summary: The paper focuses on the iterative discretization of weak formulations in the context of ODE problems. Several strategies to improve the accuracy of the method are proposed, and the method is combined with a Deferred Correction framework to introduce efficient p-adaptive modifications. Analytical and numerical results demonstrate the stability and computational efficiency of the modified methods.
APPLIED MATHEMATICS AND COMPUTATION
(2024)