Article
Computer Science, Interdisciplinary Applications
A. Rathinasamy, M. Chinnadurai, S. Athithan
Summary: The study investigates a stochastic sex-structured HIV/AIDS epidemic model with screening of infectives, showing that the model has a unique global positive solution with boundedness and permanence. Suitable Lyapunov functions are selected for investigating persistence and extinction of the disease, which is verified through numerical experiments.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2021)
Article
Mathematics, Applied
Sanaa Moussa Salman
Summary: A novel HIV/AIDS infection model was developed incorporating memory and media coverage effects, with the introduction of fractional-order derivative and time-delay for treatment simulation. The disease dies out when the basic reproduction number is less than 1, and persists when it is greater than 1.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2021)
Article
Engineering, Mechanical
Lihua Dai, Xianning Liu, Yuming Chen
Summary: This paper proposes and analyzes a fractional-order SIS model with a generalized transmission function and media coverage. The existence, uniqueness, and non-negativeness of solutions are obtained. The basic reproduction number R0 is calculated using the next generation matrix method, serving as a threshold parameter. Numerical simulations demonstrate the main theoretical results and reveal the impact of media coverage on disease transmission.
NONLINEAR DYNAMICS
(2023)
Article
Mathematics, Applied
Guodong Liu, Xinzhu Meng, Siyu Liu
Summary: This paper explores the impact of impulsive reaction-diffusion systems on lake ecological dynamics and biological structure. Through rigorous analysis and specific scenario simulations, it is found that impulsive effects have a certain influence on lake ecology.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Mathematics, Applied
Xiangyun Shi, Xiwen Gao, Xueyong Zhou, Yongfeng Li
Summary: The proposed SQEIAR model incorporates media coverage and asymptomatic infection, targeting populations with a certain level of immunity. Extinction and persistence of diseases in the model are discussed using the basic reproduction number R-C, along with an analysis of parameter thresholds and their impact on the basic reproduction number. The optimal media coverage and quarantine strategies are derived under a quadratic cost function, utilizing Pontryagin's Maximum Principle.
Article
Automation & Control Systems
Nguyen Du, Alexandru Hening, Nhu Nguyen, George Yin
Summary: This paper focuses on realistic hybrid SIR models that consider stochasticity. The proposed systems are applicable to various incidence rates used in the literature. The study analyzes a system of stochastic differential equations that include hidden state individuals and investigates the long-term behavior of the disease based on a threshold A.
NONLINEAR ANALYSIS-HYBRID SYSTEMS
(2023)
Article
Mathematics, Applied
Wenxu Ning, Zhijun Liu, Lianwen Wang, Ronghua Tan
Summary: This paper presents a stochastic mutualism model with saturation effect and pulse toxicant input, and derives a set of sufficient conditions. Analysis results are supported by numerical simulations, and the effects of various factors on the survival of species are investigated.
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
(2021)
Article
Mathematics
Qi Quan, Xiangjun Dai, Jianjun Jiao
Summary: This paper proposes a predator-prey model with impulsive diffusion and transient/nontransient impulsive harvesting. The stability and persistence of the model under simultaneous harvesting of predators and prey are investigated.
Article
Engineering, Mechanical
Tangjuan Li, Yanni Xiao
Summary: This study investigates the effects of media coverage and medical resources on disease transmission during the outbreak of emerging infectious diseases. Through the use of a mathematical model and theoretical and numerical analyses, it is found that the limitation of medical resources leads to complex dynamics in the transmission of the virus. Additionally, it is observed that saturated media coverage has little impact on the dynamics. It is suggested that providing adequate medical resources and improving media response measures can help reduce the number of infections.
NONLINEAR DYNAMICS
(2022)
Article
Mathematics, Interdisciplinary Applications
Abdulwasea Alkhazzan, Jungang Wang, Yufeng Nie, Hasib Khan, Jehad Alzabut
Summary: This study proposes a novel epidemic model that considers the impact of transport-related infection, media coverage, and Levy noise. The researchers investigate the existence of a positive global solution and derive sufficient conditions for disease extinction and persistence. By analyzing the influence of various parameters on the model's dynamics, the study provides important insights into the science of epidemiology and lays the groundwork for improved methods of disease prevention.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Mathematics, Applied
Chen Qianjun, Liu Zijian, Tan Yuanshun, Yang Jin
Summary: A stochastic hybrid population model with Allee effect, Markovian switching, and impulsive perturbations is proposed and studied in this paper. The conditions for extinction and permanence are obtained, and some asymptotic properties are investigated.
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
(2023)
Article
Mathematics
Jinxing Zhao, Yuanfu Shao
Summary: In this paper, a Holling-Leslie predator-prey system with impulsive and stochastic disturbance is proposed and analyzed using numerical simulations and mathematical methods. The research focuses on the existence, stability, and stochastic permanence of the system.
JOURNAL OF MATHEMATICS
(2021)
Article
Mathematics, Applied
Long Zhang, Xiaolin Fan, Zhidong Teng
Summary: This paper investigates a class of nonautonomous SEIRS epidemic models with vaccination and nonlinear incidence. New threshold values for disease extinction and permanence are established under weak assumptions, in the form of integrals; special cases of autonomous, periodic, and almost periodic circumstances are discussed, with necessary and sufficient criteria obtained for disease extinction and permanence. Numerical examples and simulations are provided to illustrate the analytic results.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Mathematical & Computational Biology
Siyu Chen, Zhijun Liu, Ronghua Tan, Lianwen Wang
Summary: A system of impulsive stochastic differential equations is proposed as a model for two-species facultative mutualism subject to impulsive and two coupling noise source perturbations, taking saturation effect into account. Sufficient criteria for extinction and permanence of the system are established, supported by extensive simulation figures. Effects of coupling white noises, impulses, growth rates, competition rates, and mutualism rates on population survival are also studied.
INTERNATIONAL JOURNAL OF BIOMATHEMATICS
(2021)
Article
Mathematics
Ahmadjan Muhammadhaji, Yimamu Maimaiti
Summary: This paper studies a non-autonomous competition and cooperation model of two enterprises with discrete time delays and feedback controls. New criteria for analyzing permanence, periodic solution, and global attractiveness are proposed. Common mathematical techniques such as the Lyapunov method, the continuation theorem, and the comparison principle are used. The concept of permanence, which refers to the long-term survival of the enterprises within the competitive and cooperative framework, is investigated using the comparison principle and inequality techniques. Conditions for exhibiting periodic behavior are established using the continuation theorem. Global attractiveness of the system is derived by constructing multiple Lyapunov functionals. An example is presented to demonstrate the applicability and validity of the proposed criteria.
Article
Mathematics, Applied
Hao Liu, Yuzhe Li
Summary: This paper investigates the finite-time stealthy covert attack on reference tracking systems with unknown-but-bounded noises. It proposes a novel finite-time covert attack method that can steer the system state into a target set within a finite time interval while being undetectable.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Nikolay A. Kudryashov, Aleksandr A. Kutukov, Sofia F. Lavrova
Summary: The Chavy-Waddy-Kolokolnikov model with dispersion is analyzed, and new properties of the model are studied. It is shown that dispersion can be used as a control mechanism for bacterial colonies.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Qiang Ma, Jianxin Lv, Lin Bi
Summary: This paper introduces a linear stability equation based on the Boltzmann equation and establishes the relationship between small perturbations and macroscopic variables. The numerical solutions of the linear stability equations based on the Boltzmann equation and the Navier-Stokes equations are the same under the continuum assumption, providing a theoretical foundation for stability research.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Samuel W. Akingbade, Marian Gidea, Matteo Manzi, Vahid Nateghi
Summary: This paper presents a heuristic argument for the capacity of Topological Data Analysis (TDA) to detect critical transitions in financial time series. The argument is based on the Log-Periodic Power Law Singularity (LPPLS) model, which characterizes financial bubbles as super-exponential growth (or decay) with increasing oscillations approaching a tipping point. The study shows that whenever the LPPLS model fits the data, TDA generates early warning signals. As an application, the approach is illustrated using positive and negative bubbles in the Bitcoin historical price.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Xavier Antoine, Jeremie Gaidamour, Emmanuel Lorin
Summary: This paper is interested in computing the ground state of nonlinear Schrodinger/Gross-Pitaevskii equations using gradient flow type methods. The authors derived and analyzed Fractional Normalized Gradient Flow methods, which involve fractional derivatives and generalize the well-known Normalized Gradient Flow method proposed by Bao and Du in 2004. Several experiments are proposed to illustrate the convergence properties of the developed algorithms.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Lianwen Wang, Xingyu Wang, Zhijun Liu, Yating Wang
Summary: This contribution presents a delayed diffusive SEIVS epidemic model that can predict and quantify the transmission dynamics of slowly progressive diseases. The model is applied to fit pulmonary tuberculosis case data in China and provides predictions of its spread trend and effectiveness of interventions.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Shuangxi Huang, Feng-Fei Jin
Summary: This paper investigates the error feedback regulator problem for a 1-D wave equation with velocity recirculation. By introducing an invertible transformation and an adaptive error-based observer, an observer-based error feedback controller is constructed to regulate the tracking error to zero asymptotically and ensure bounded internal signals.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Weimin Liu, Shiqi Gao, Feng Xu, Yandong Zhao, Yuanqing Xia, Jinkun Liu
Summary: This paper studies the modeling and consensus control of flexible wings with bending and torsion deformation, considering the vibration suppression as well. Unlike most existing multi-agent control theories, the agent system in this study is a distributed parameter system. By considering the mutual coupling between the wing's deformation and rotation angle, the dynamics model of each agent is expressed using sets of partial differential equations (PDEs) and ordinary differential equations (ODEs). Boundary control algorithms are designed to achieve control objectives, and it is proven that the closed-loop system is asymptotically stable. Numerical simulation is conducted to demonstrate the effectiveness of the proposed control scheme.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Gourav Mandal, Lakshmi Narayan Guin, Santabrata Chakravarty
Summary: The ecological framework investigates the dynamical complexity of a system influenced by prey refuge and alternative food sources for predators. This study provides a thorough investigation of the stability-instability phenomena, system parameters sensitivity, and the occurrence of bifurcations. The bubbling phenomenon, which indicates a change in the amplitudes of successive cycles, is observed in the current two-dimensional continuous system. The controlling system parameter for the bubbling phenomena is found to be the most sensitive. The prediction and identification of bifurcations in the dynamical system are crucial for theoretical and field researchers.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Damian Trofimowicz, Tomasz P. Stefanski, Jacek Gulgowski, Tomasz Talaska
Summary: This paper presents the application of control engineering methods in modeling and simulating signal propagation in time-fractional electrodynamics. By simulating signal propagation in electromagnetic media using Maxwell's equations with fractional-order constitutive relations in the time domain, the equations in time-fractional electrodynamics can be considered as a continuous-time system of state-space equations in control engineering. Analytical solutions are derived for electromagnetic-wave propagation in the time-fractional media based on state-transition matrices, and discrete time zero-order-hold equivalent models are developed and their analytical solutions are derived. The proposed models yield the same results as other reference methods, but are more flexible in terms of the number of simulation scenarios that can be tackled due to the application of the finite-difference scheme.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Yuhao Zhao, Fanhao Guo, Deshui Xu
Summary: This study develops a vibration analysis model of a nonlinear coupling-layered soft-core beam system and finds that nonlinear coupling layers are responsible for the nonlinear phenomena in the system. By using reasonable parameters for the nonlinear coupling layers, vibrations in the resonance regions can be reduced and effective control of the vibration energy of the soft-core beam system can be achieved.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
S. Kumar, H. Roy, A. Mitra, K. Ganguly
Summary: This study investigates the nonlinear dynamic behavior of bidirectional functionally graded plates (BFG) and unidirectional functionally graded plates (UFG). Two different methods, namely the whole domain method and the finite element method, are used to formulate the dynamic problem. The results show that all three plates exhibit hardening type nonlinearity, with the effect of material gradation parameters being more pronounced in simply supported plates.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Isaac A. Garcia, Susanna Maza
Summary: This paper analyzes the role of non-autonomous inverse Jacobi multipliers in the problem of nonexistence, existence, localization, and hyperbolic nature of periodic orbits of planar vector fields. It extends and generalizes previous results that focused only on the autonomous or periodic case, providing novel applications of inverse Jacobi multipliers.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Yongjian Liu, Yasi Lu, Calogero Vetro
Summary: This paper introduces a new double phase elliptic inclusion problem (DPEI) involving a nonlinear and nonhomogeneous partial differential operator. It establishes the existence and extremality results to the elliptic inclusion problem and provides definitions for weak solutions, subsolutions, and supersolutions.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Shangshuai Li, Da-jun Zhang
Summary: In this paper, the Cauchy matrix structure of the spin-1 Gross-Pitaevskii equations is investigated. A 2 x 2 matrix nonlinear Schrodinger equation is derived using the Cauchy matrix approach, serving as an unreduced model for the spin-1 BEC system with explicit solutions. Suitable constraints are provided to obtain reductions for the classical and nonlocal spin-1 GP equations and their solutions, including one-soliton solution, two-soliton solution, and double-pole solution.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)