Article
Mathematics, Applied
Jia Liu, Jing Chen, Canrong Tian
Summary: By introducing a weighted networked structure and analyzing the amplitude equation, this study investigates the Turing bifurcation in the classical reaction-diffusion system, demonstrating its existence with large diffusion rates and stability. The findings suggest the importance of network structures in understanding complex dynamics in reaction-diffusion systems.
APPLIED MATHEMATICS LETTERS
(2021)
Article
Mathematics, Interdisciplinary Applications
Feifan Zhang, Yingxin Li, Yilong Zhao, Zezheng Liu
Summary: This study explores the effects of sand movements on vegetation diffusion and pattern formation. Theoretical analysis and numerical simulations reveal that under the influence of cross-diffusion, vegetation patterns can transition from stripes to spots, with hysteresis observed during the pattern transition process.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2022)
Article
Mathematics, Interdisciplinary Applications
Malay Banerjee, Swadesh Pal, Pranali Roy Chowdhury
Summary: This paper investigates the spatio-temporal pattern formation in a complex habitat. The results show that the shape and size of the habitat play a significant role in determining the spatio-temporal patterns.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Mathematical & Computational Biology
Subrata Dey, Malay Banerjee, Saktipada Ghorai
Summary: A prey-predator model with a generalist predator and Holling type-II functional response exhibits complex dynamics, including bistability, tristability, and various global and local bifurcations. The presence of a generalist predator reduces predation pressure on the focal prey species, leading to increased stability. The model also shows the existence of steady state solutions for suitable parameter values in a spatio-temporal diffusive system. Weakly nonlinear analysis and numerical simulations confirm the analytical results and identify bifurcations of stable stationary patch solutions and dynamic pattern solutions in the Turing and Turing-Hopf regions.
MATHEMATICAL MODELLING OF NATURAL PHENOMENA
(2022)
Article
Mathematics, Interdisciplinary Applications
Feifan Zhang, Hao Tian, Hongfan Zhao, Xinran Zhang, Qiyu Shi
Summary: This study explored a discrete model involving toxic phytoplankton and zooplankton, considering the Allee effect and cross-diffusion. By analyzing the flip, Neimark-Sacker, and Turing bifurcations under different parameter conditions, the potential for pattern formation was revealed. Numerical simulations confirmed the theoretical results, showing the emergence of special patterns.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2022)
Article
Mathematics, Applied
Fethi Souna, Pankaj Kumar Tiwari, Mustapha Belabbas, Youssaf Menacer
Summary: In this paper, the intrinsic impact of the predator-taxis coefficient on the formation of spatial patterns in a predator-prey system with prey social behavior subject to Neumann boundary conditions is investigated. The Turing pattern is found to be fully captured by three distinct critical thresholds, and the direction of Turing bifurcation is established through weakly nonlinear analysis and the amplitude equation. The mathematical analysis reveals that the inclusion of the predator-taxis coefficient in the predator-prey system may lead to the emergence of either subcritical or supercritical Turing bifurcation. Numerical experiments confirm the theoretical findings and exhibit various spatial patterns with different values of predator-taxis coefficients.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Interdisciplinary Applications
Sounov Marick, Santanu Bhattacharya, Nandadulal Bairagi
Summary: In this study, the spatiotemporal dynamics of a predator-prey model with selective nonlinear saturated harvesting were investigated. The analysis of both local and global bifurcations in the non-diffusive system revealed that the system may undergo transcritical, Hopf, saddle-node, and homoclinic bifurcations with changes in carrying capacity and harvesting efforts. Simulation results showed that the paradox of enrichment may be eliminated in a harvested system with higher carrying capacity. The spatiotemporal study identified different pattern-forming instabilities, established a critical ratio of predator to prey diffusivities for Turing instability occurrence, and derived an amplitude equation and predicted the pattern's form through weakly nonlinear analysis. The main findings of this work were that prey harvesting promotes spatiotemporal chaos controlled by predator diffusion, intensive prey harvesting causes spatial segregation, and predator harvesting relaxes it. It was also observed that spatial segregation enhances overall species biomass. A unique observation in this study was the occurrence and nonoccurrence of spatiotemporal chaos in the Hopf-Turing parametric space.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Mathematics, Interdisciplinary Applications
Xiaoling Han, Ceyu Lei
Summary: This work investigates a discrete predator-prey system with periodic boundary conditions. The existence, local stability, and global stability of the equilibrium points of the system are examined. The criteria for flip bifurcation and Neimark-Sacker bifurcation are obtained, as well as the conditions for Turing instability when population self-diffusion occurs. Numerical simulation is used to study the impact of diffusion coefficient and prey's natural growth rate on system dynamics.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Mathematics, Applied
Linhe Zhu, Le He
Summary: The paper presents an example of a reaction-diffusion model defined on continuous space to study common problems under Turing instability. It analyzes the necessary conditions for Turing instability and the theoretical conditions for the appearance of specific patterns near Turing bifurcation. The numerical simulations confirm the correctness of the theoretical analysis and find that the pattern type can be changed by the cross-diffusion coefficient.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2022)
Article
Mathematics, Interdisciplinary Applications
Fatao Wang, Ruizhi Yang
Summary: In this paper, we investigate a cross-diffusion predator-prey system with Holling type functional response. We analyze the local stability, Turing instability, spatial pattern formation, Hopf and Turing-Hopf bifurcation of the equilibrium. Numerical simulation reveals that the system experiences cross-diffusion-driven instability and exhibits various patterns such as spots, stripe-spot mixtures, and labyrinthine patterns. The study also shows that the intrinsic growth rate coefficient and the environmental carrying capacity coefficient are crucial factors for the stability of the predator-prey system.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Mathematics, Interdisciplinary Applications
Shivam, Teekam Singh, Mukesh Kumar
Summary: This paper studies the temporal and spatiotemporal dynamics of a three-level food web system and explores the stability of the system and the development of Turing patterns using methods like Jacobian analysis and multiple-scale analysis. The findings can serve as a baseline for ecological model research.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2022)
Article
Engineering, Mechanical
Mengxin Chen
Summary: This paper investigates the spatiotemporal inhomogeneous pattern phenomenon of a predator-prey model with chemotaxis and time delay. The study provides sufficient conditions to ensure the existence of Turing instability by adjusting the control parameters of time delay and chemotaxis. It also determines the occurrence conditions of Turing-Hopf bifurcation using time delay control parameter and chemotaxis sensitivity coefficient. The research shows that both time delay and chemotaxis can affect the formation of spatiotemporal inhomogeneous patterns.
NONLINEAR DYNAMICS
(2023)
Article
Engineering, Mechanical
Mengxin Chen
Summary: In this paper, the spatiotemporal inhomogeneous pattern phenomenon of a predator-prey model with chemotaxis and time delay is investigated. The precise intervals of the Turing instability are determined, and sufficient conditions for its existence are obtained by adjusting the control parameters. Numerical experiments show that both the time delay control parameter and chemotaxis sensitivity coefficient can affect the formation of the patterns.
NONLINEAR DYNAMICS
(2023)
Article
Computer Science, Information Systems
Junlang Hu, Linhe Zhu, Miao Peng
Summary: In this paper, a rumor propagation dynamic model with Allee effect and cross-diffusion is proposed, and a general form of cross-diffusion model with time delay is analyzed. The amplitude equation for the general form of weakly nonlinear models is derived using the Multiple Scale Analysis method. The correctness of the theoretical analysis is verified through numerical simulations.
INFORMATION SCIENCES
(2022)
Article
Mathematics, Applied
Yansu Ji, Jianwei Shen, Xiaochen Mao
Summary: This paper investigates the pattern dynamics of reaction-diffusion systems with time delay, and obtains the conditions for Hopf bifurcation and Turing instability. The derived amplitude equation and numerical simulations verify the theoretical results.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S
(2023)
Article
Mathematical & Computational Biology
Jing Xu, Sanling Yuan, Tonghua Zhang
Summary: This paper investigates the effects of environmental perturbations on the growth of water hyacinth and fish species, as well as their economic values. By establishing a model and conducting numerical simulations, the study demonstrates that fuzzy parameters can affect the optimal harvesting strategy.
INTERNATIONAL JOURNAL OF BIOMATHEMATICS
(2023)
Article
Biology
Shengqiang Zhang, Xichao Duan, Tonghua Zhang, Sanling Yuan
Summary: Biological invasions pose serious threats to ecosystem stability, biodiversity, and human health, but there are few effective measures for controlling them. By constructing a stochastic host-generalist parasitoid model, this study reveals that generalist parasitoids are more vulnerable to environmental noises compared to invasive hosts, and the prevention and control effects of biological control on invasive hosts are closely related to the initial population sizes.
BULLETIN OF MATHEMATICAL BIOLOGY
(2023)
Article
Mathematics, Interdisciplinary Applications
Guijie Lan, Baojun Song, Sanling Yuan
Summary: An SEIR epidemic model incorporating both environmental and genetic factors is developed to investigate the impact of Markovian switching on the transmission dynamics of infectious diseases. The model shows that the basic reproduction number R0 serves as a sharp threshold for disease transmission, with the disease dying out when R0 < 1 and persisting when R0 > 1. The Markov process derived from the model exhibits positive Harris recurrence if R0 > 1, along with global attractivity and ergodicity.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Mathematics, Applied
Yu Yang, Tonghua Zhang, Jinling Zhou
Summary: This paper investigates the global stability of disease-free steady state for a degenerate reaction-diffusion host-pathogen model with spatial heterogeneity when R0 = 1. The study is a continuation of the work by Wang and Dai (2022).
APPLIED MATHEMATICS LETTERS
(2023)
Article
Mathematics, Interdisciplinary Applications
Anji Yang, Hao Wang, Sanling Yuan
Summary: This paper investigates the negative impacts of critical transitions on ecosystem services and human economies. It proposes a method to track the true state of a predator-prey model under noisy fluctuations and determines tipping times for population collapse. The results show that disturbance events and predator growth rate significantly influence the stability and biodiversity of the ecosystem. Quasi-potential analysis confirms the results obtained from tipping time analysis.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Mathematics, Interdisciplinary Applications
Jianxin Chen, Rui Hou, Lu Xiao, Tonghua Zhang, Yongwu Zhou
Summary: Considering corporate social responsibility, this paper examines the equilibrium strategies of a closed-loop supply chain consisting of a manufacturer, a fairness-concerned retailer, and a capital-constrained recycler in both static and dynamic frameworks. The study incorporates supply chain financing and fairness concerns and explores the complex dynamics and impacts of parameters on decision-making and system stability.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Ecology
Anglu Shen, Shufei Gao, Christopher M. Heggerud, Hao Wang, Zengling Ma, Sanling Yuan
Summary: Studying the interaction between algal growth and their photo-physiology is crucial for understanding harmful algal blooms. By using pulse amplitude modulated fluorometry, we observed variations in cell abundance and chlorophyll fluorescence parameters during the formation of Prorocentrum shikokuense algal blooms. Based on this interaction, we developed a new algal growth model incorporating cell growth delay. These results have important implications for understanding the relationship between phytoplankton growth dynamics and photosynthetic parameters and can aid in predicting and managing harmful algal blooms.
ECOLOGICAL MODELLING
(2023)
Article
Mathematics
Shuai Li, Sanling Yuan, Zhen Jin, Hao Wang
Summary: In this paper, a spatial model with prey memory delay, Allee effect, and predator maturation delay is formulated. The model undergoes a saddle-node bifurcation at the tipping point of Allee effect intensity. By analyzing the stability of the coexistence steady state without delays, crossing curves on the delays plane are obtained, indicating the occurrence of Hopf bifurcation when delays pass through these curves. The model exhibits multiple stability switches and a stable spatially heterogeneous periodic solution with mode-4 as delays vary.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2023)
Article
Mathematics, Applied
Jing Xu, Sanling Yuan
Summary: This paper develops a stochastic pine wilt disease model with prevention strategies to obtain the conditions for its near-optimal control. By decreasing the infected pine forests and beetle population while minimizing the costs of prevention strategies, the near-optimality problem is constructed. The necessary conditions of the near-optimal control are derived using the spike variational technique. An example is presented to illustrate the validity of the main theoretical results, showing that reasonable prevention strategies can effectively reduce pine wilt infection, protect pine forests, and reduce economic losses.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Review
Cardiac & Cardiovascular Systems
Tian-Ping Yu, Jing Hou, Ting-Jie Yang, Xue-Qin Chen, Yu-Cheng Chen
Summary: This study reports the genotypes and phenotypes of hereditary transthyretin cardiac amyloidosis (hATTR-CA) in a Western Chinese cohort and reviews the genetic profiles of this disorder in the Chinese population. The study identified a novel TTR variant causing hATTR-CA in the West Han Chinese population. The findings highlight the importance of early genotypic screening and biopsy for timely diagnosis of hATTR-CA.
Article
Engineering, Multidisciplinary
Tingting Yu, Sanling Yuan
Summary: In this article, we propose a delayed tree population model with non-smooth continuous threshold harvesting. We classify the existence and number of positive equilibrium points by addressing the difficulties caused by the nonlinear term and the time delay. We analyze the stability of the model, including local and global asymptotic stability of the equilibria, bistability, and stability switches occurring at the positive equilibrium, using the domain-decomposition method and Hopf bifurcation theory. Furthermore, we investigate the influence of the maturation delay of trees on optimal harvesting and find that the model exhibits chaotic-like oscillations, long transients, and regime shifts with increasing maturation delay or harvesting rate, and can even have multi-types of tristability.
APPLIED MATHEMATICAL MODELLING
(2023)
Article
Mathematics, Applied
Shuai Li, Sanling Yuan
Summary: In this letter, we study double Hopf bifurcations triggered by gestation and memory delays in a spatial model with tactical directed movement. We generalize the calculation algorithm of normal form for double Hopf bifurcation to a spatial model with different delays in both reaction and advection terms. We then classify the dynamics around the double Hopf bifurcation points into 6 categories and observe the coexistence of stable periodic orbits with different spatial modes.
APPLIED MATHEMATICS LETTERS
(2023)
Article
Biology
Cuihua Wang, Hao Wang, Sanling Yuan
Summary: Precipitation is crucial for vegetation growth in arid or semi-arid environments, and recent research has found that vegetation growth has a lag effect in response to precipitation. A study on a water-vegetation model with spatiotemporal nonlocal effects reveals that the temporal kernel function does not impact Turing bifurcation. The study also shows that time delay and spatial nonlocal competition can have various effects on vegetation pattern formation, such as postponing evolution, inducing stability switches, and triggering the emergence of traveling wave patterns.
JOURNAL OF MATHEMATICAL BIOLOGY
(2023)
Article
Mathematics, Applied
Guijie Lan, Sanling Yuan
Summary: In this paper, a stochastic SIRS model with density-dependent demographics is proposed to study the dynamics of infectious disease transmission under stochastic environmental fluctuations. The position of the basic reproduction number R0 with respect to 1 is shown to be the threshold between disease extinction and persistence under mild extra conditions. As an application, the parameter values of the model are estimated using 2017 influenza A data, and the effect of random noises on the dynamics of the model is investigated. The study reveals different correlations of R0 with noise intensity for the infected and susceptible populations compared to existing literature findings.
STUDIES IN APPLIED MATHEMATICS
(2023)
Article
Fisheries
Yingjie Fei, Shenglong Yang, Mengya Huang, Xiaomei Wu, Zhenzhen Yang, Jiangyue Zhao, Fenghua Tang, Wei Fan, Sanling Yuan
Summary: Understanding the spatial distribution of fishing activity and suitable fishing areas is crucial for sustainable fisheries management. This study developed habitat suitability index models using marine environmental data to identify climate-related habitat changes and variations in the distribution of fishing activity for squid-jigging vessels in the Northwest Pacific Ocean. The results showed significant seasonal changes in suitable fishing areas, and the weighted arithmetic mean method performed better in predicting fishing activity. The study emphasizes the importance of managing high fishing pressure areas and acknowledges the limitations of fishery data.
Article
Mathematics, Interdisciplinary Applications
Bo Li, Tian Huang
Summary: This paper proposes an approximate optimal strategy based on a piecewise parameterization and optimization (PPAO) method for solving optimization problems in stochastic control systems. The method obtains a piecewise parameter control by solving first-order differential equations, which simplifies the control form and ensures a small model error.
CHAOS SOLITONS & FRACTALS
(2024)
Article
Mathematics, Interdisciplinary Applications
Guram Mikaberidze, Sayantan Nag Chowdhury, Alan Hastings, Raissa M. D'Souza
Summary: This study explores the collective behavior of interacting entities, focusing on the co-evolution of diverse mobile agents in a heterogeneous environment network. Increasing agent density, introducing heterogeneity, and designing the network structure intelligently can promote agent cohesion.
CHAOS SOLITONS & FRACTALS
(2024)
Article
Mathematics, Interdisciplinary Applications
Gengxiang Wang, Yang Liu, Caishan Liu
Summary: This investigation studies the impact behavior of a contact body in a fluidic environment. A dissipated coefficient is introduced to describe the energy dissipation caused by hydrodynamic forces. A new fluid damping factor is derived to depict the coupling between liquid and solid, as well as the coupling between solid and solid. A new coefficient of restitution (CoR) is proposed to determine the actual physical impact. A new contact force model with a fluid damping factor tailored for immersed collision events is proposed.
CHAOS SOLITONS & FRACTALS
(2024)
