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
Engineering, Mechanical
Haojie Liu, Xiumin Gao
Summary: This study investigates the time-delayed feedback control for a rectangular prism undergoing galloping under wind excitation. By using mathematical models and stability analysis, it is found that delayed acceleration feedback can achieve multiple control objectives and change bifurcation behavior.
NONLINEAR DYNAMICS
(2021)
Article
Mathematics, Interdisciplinary Applications
Linhe Zhu, Wenxin Zheng, Shuling Shen
Summary: This paper studies a rumor transmission model with a nonlinear transmission rate and a non-smooth threshold transmission function based on the classical SI infectious disease model. The existence of model solutions is proven and the number of non-negative equilibrium points is obtained. The equilibrium points' characteristic equations are discussed by dividing the model into spatially homogeneous and inhomogeneous parts with continuous and discontinuous, and the conditions for Saddle-node bifurcation, Turing bifurcation, and Hopf bifurcation are obtained under the corresponding conditions. Finally, the simulation results further verify the feasibility of the theoretical calculation results.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Biochemical Research Methods
Chengxian Li, Haihong Liu, Tonghua Zhang, Yuan Zhang
Summary: This paper investigates a model of miR-9/Hes1 interaction network with time delay and diffusion effect. The stability of the positive equilibrium and the existence of local Hopf bifurcation and Turing-Hopf bifurcation are analyzed. An algorithm for determining the direction, stability, and period of the corresponding bifurcating periodic solutions is presented. The results show that time delay can induce oscillation in quiescent progenitors but has little effect on the differentiated state. The integrated effect of delay and diffusion can lead to spatially inhomogeneous patterns. Moreover, spatially homogeneous/inhomogeneous periodic solutions can coexist when the diffusion coefficients are appropriately small.
IEEE-ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS
(2022)
Article
Physics, Multidisciplinary
Wang Nan, Xiao Min, Jiang Hai-Jun, Huang Xia
Summary: This paper proposes a social network rumor spreading model that considers both reaction diffusion and fermentation time delay, and studies the effects of spatial diffusion and time delay on rumor spreading in online social networks. The existence of equilibrium point and basic reproduction number of the model are analyzed, and the local stability and influence of diffusion on system stability are discussed. The Hopf bifurcation condition of the model with time delay is established, and the numerical simulation results show the importance of diffusion and time delay in the dynamic evolution of rumor spreading. The impact of the crowding degree of spreaders on rumor propagation is also simulated.
ACTA PHYSICA SINICA
(2022)
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
Changchun Liu, Ming Mei, Jiaqi Yang
Summary: This paper focuses on a class of nonlocal reaction-diffusion equations with time-delay and degenerate diffusion. It is shown that the Cauchy problem of the equation possesses a Holder-continuous solution affected by the degeneracy of diffusion. Additionally, non-critical traveling waves are proven to be globally L-1-stable, with a derived time-exponential convergence rate. The approach used for the proof combines technical L-1-weighted energy estimates with compactness analysis, incorporating new developments.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2022)
Article
Mathematics, Interdisciplinary Applications
Yehu Lv, Zhihua Liu
Summary: In this paper, a diffusive Brusselator model with gene expression time delay is proposed and its bifurcation behavior is studied. The conditions for Turing instability are derived, and the spatiotemporal dynamics in six different regions of the parameter plane are analyzed.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics, Interdisciplinary Applications
Peng Zhu, Min Xiao, Xia Huang, Fuchen Zhang, Zhen Wang, Jinde Cao
Summary: In recent years, the control of time evolution in ordinary differential systems has developed rapidly, while the control of spatiotemporal evolution dynamics in partial differential systems remains an open question. Turing pattern is a main spatiotemporal evolution behavior in mussel-algal ecosystems and controlling it can restore the ecosystem's stability. However, there has been limited research on the optimal control of Turing pattern in the mussel-algal system. This paper proposes a proportional-derivative (PD) control strategy for the reaction-diffusion mussel-algae model with time delays and demonstrates its efficiency and feasibility through numerical simulations.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Mathematics, Applied
Agnieszka Bartlomiejczyk, Marek Bodnar
Summary: This study focuses on a mathematical model of gene transcription and protein synthesis with negative feedback. The model considers the formation of dimers, the binding of dimers to DNA, and the time delay in the translation process. By analyzing a system of three ordinary differential equations with time delay, the study provides conditions for the stability of the positive steady state and the existence of the Hopf bifurcation. The influence of the delay in the transcription process on the model dynamics is investigated, and conditions determining the type of bifurcation and stability of the resulting limit cycle are formulated.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics
Xinggui Li, Xinsong Yang
Summary: This paper investigates the global stability of an impulsive advertising dynamic model considering the influence of diffusion. It employs variational methods to ensure the unique existence of equilibrium points in the infinite dimensional function space, and derives a global stability criterion of the system through the impulse inequality lemma and orthogonal decomposition of a class of Sobolev spaces. Numerical simulations validate the effectiveness of the proposed method.
Article
Mathematics, Interdisciplinary Applications
Xiaosong Tang, Xiaoyu Zhang, Yiting Liu, Wankun Li, Qi Zhong
Summary: In this paper, the dynamical behavior of a delayed diffusive cooperative species model with cross-diffusion is investigated. The persistence properties and global stability of positive equilibrium for this model are studied in the case of self-diffusion, and it is found that the delay has no effect on the stability of positive equilibrium, while cross-diffusion can affect it. Moreover, Turing bifurcation on one-dimensional space and Turing pattern on two-dimensional space are discussed, and different patterns are obtained through numerical simulations.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Mathematics, Interdisciplinary Applications
Huan Su, Jing Xu
Summary: In this paper, time-delayed sampled-data feedback control technique is used to asymptotically stabilize a class of unstable delayed differential systems. An effective interval of the control parameter is obtained for a given sampling period through the analysis of eigenvalues distribution change. The upper bound of the sampling period is estimated using the practical criterion for the size of the sampling period.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2021)
Article
Mathematical & Computational Biology
Tingting Ma, Xinzhu Meng
Summary: In this study, we investigated a new cross-diffusive prey-predator system that takes into account prey refuge, fear effect, and predator cannibalism. Through theoretical analysis and numerical simulations, we found that establishing prey refuge can effectively protect the growth of prey. We also explored the system's properties such as persistence, stability, bifurcation, and Turing instability.
MATHEMATICAL BIOSCIENCES AND ENGINEERING
(2022)
Article
Materials Science, Multidisciplinary
Qing Li, Deguo Sun, Hongxia Liu, Wencai Zhao
Summary: This paper proposes a delayed feedback control strategy for a fractional ecological infectious disease system with infected predators. The results show that selecting a suitable feedback controller can effectively extend the stable domain of the system. The accuracy and effectiveness of the delay feedback controller in controlling the bifurcation are verified through numerical simulations.
RESULTS IN PHYSICS
(2023)
