Table of Content

  

20 October 2023
Volume 58 Issue 10

Peak value and peak time of nonlinear heterogeneous epidemic model

Shengqiang LIU,Ningjuan MA

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2023, 58(10):  1-12.  doi:10.6040/j.issn.1671-9352.0.2023.340

Abstract ( 257 )   HTML ( 15 )   PDF (2578KB) ( 319 )   Save

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The study focuses on analyzing the transmission mechanisms of nonlinear heterogeneous epidemic models within a short-time frame. As a result, novel criteria for determining the peak value and peak time of a heterogeneous epidemic model are achieved, and numerical fitting is applied to prove the efficient of the mold.

Global dynamics analysis of a class of Filippov-type HR neuron model

Wenyan LIU,Shuai QIAO,Chenghua GAO

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2023, 58(10):  13-23.  doi:10.6040/j.issn.1671-9352.0.2022.319

Abstract ( 172 )   HTML ( 0 )   PDF (6675KB) ( 133 )   Save

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Based on the HR neuron model under electromagnetic radiation, a non-smooth control strategy is proposed, in which the membrane potential is utilized as the threshold to determine the switching function corresponding to the electromagnetic induction intensity and external stimulus current. Consequently, a four-dimensional Filippov-type HR neuron model is established. Firstly, the existence, stability, and global bifurcation behaviors of equilibrium points of two subsystems are discussed by using stability theory and numerical simulation. Then, the bistable behavior and evolution modes of subsystems are investigated based on the two-parameter bifurcation analysis. Further, the existence of various equilibrium points and sliding mode dynamics of the system is analyzed by Filippov convex combination method and Utkin's equivalent control method. Finally, the sliding firing modes and bistable features under threshold control strategy are revealed by the method of fast-slow variable dissection.

Parameter estimation for competitive Lotka-Volterra model with Lévy noise

Shimiao ZHANG,Yan LYU

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2023, 58(10):  24-31.  doi:10.6040/j.issn.1671-9352.0.2023.151

Abstract ( 163 )   HTML ( 0 )   PDF (572KB) ( 107 )   Save

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Based on the principle of least square and the technique of discretization, parameter estimation problem for stochastic two-species Lotka-Volterra competitive system driven by Lévy noise is studied. The least squares estimator is proved to be asymptotic consistent in the case ε→0 and n→∞, and the asymptotic distribution of the estimator is obtained. Finally, the numerical simulation for the estimators of the competitive model is given, and the results are in line with the theory.

Hopf bifurcation of a vegetation-water reaction-diffusion model with time delay

Gaihui GUO,Jingjing WANG,Wangrui LI

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2023, 58(10):  32-42, 53.  doi:10.6040/j.issn.1671-9352.0.2023.279

Abstract ( 172 )   HTML ( 6 )   PDF (3010KB) ( 201 )   Save

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Taking the time delay τ as the bifurcation parameter, the effect of time delay on the stability of the positive steady state point and the existence of Hopf bifurcation are given by analyzing the characteristic equation. The criteria for the direction of Hopf bifurcation and the stability of periodic solutions are obtained by the normal form theory and the center manifold theorem. Finally, the theoretical results are verified by numerical simulations.

Dynamics of a reaction-diffusion predator-prey model incorporating prey refuge and fear effect

Qian CAO,Yanling LI,Weihua SHAN

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2023, 58(10):  43-53.  doi:10.6040/j.issn.1671-9352.0.2022.308

Abstract ( 153 )   HTML ( 3 )   PDF (5701KB) ( 255 )   Save

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For a reaction-diffusion predator-prey system with prey refuge and fear effect, the Turing instability of the positive constant solution for the system and a priori estimates of solutions for the system are investigated. It is proved that there is no nonconstant positive steady-state solution for the system under certain parameter conditions. Moreover, taking the diffusion coefficient of the predator as the bifurcation parameter, the global structure of the bifurcation solution is constructed. It is found that the bifurcation solution can be extended to infinity when the diffusion coefficient of predator is greater than some critical value. Finally, by numerical simulations, the theoretical results are verified and supplemented.

Dynamics of a stochastic predation model with fear effect and Crowley-Martin functional response

Yuke ZHANG,Xinzhu MENG

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2023, 58(10):  54-66.  doi:10.6040/j.issn.1671-9352.0.2022.635

Abstract ( 157 )   HTML ( 3 )   PDF (3470KB) ( 90 )   Save

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A stochastic predator-prey model with fear effect and Crowley-Martin functional response is studied. We first give the existence and uniqueness of global positive solutions and the boundedness of solutions on the stochastic model. We explore sufficient conditions for the persistence in mean and the extinction of the populations by using stochastic qualitative analysis theory. The existence of unique ergodic stationary distribution is proved by establishing suitable Lyapunov functions. Finally, numerical simulations are conducted to reveal the effects of fear and white noise on the theoretical results of population dynamics.

Exponential stability of reaction-diffusion Cohen-Grossberg neural networks with Dirichlet boundary conditions

Lei LI,Yongsheng YE

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2023, 58(10):  67-74.  doi:10.6040/j.issn.1671-9352.0.2023.157

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By constructing a suitable Lyapunov functional and combining it with mathematical analysis techniques, we discuss the exponential stability of impulsive time delay reaction-diffusion Cohen-Grossberg neural networks with Dirichlet boundary conditions and Markovian switching. Some sufficient criteria for exponential stability of neural networks are obtained by using the inequality technique and stochastic analysis theory. Finally, an example is given to verify the validity of the results.

Optimal birth control of n species nonlinear competition system with age-structure

Zijuan ZHOU,Zhixue LUO

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2023, 58(10):  75-83.  doi:10.6040/j.issn.1671-9352.0.2023.207

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The optimal birth control of n species nonlinear competition system with age-structure is investigated. The existence and uniqueness of non-negative solution of the system is proved by using the fixed-point theorem. The extremization sequence is constructed, and Mazur?s theorem are used to verify the existence of the optimal solution of the optimal birth control problem, and the necessity conditions are derived out via normal cone and conjugate system techniques.

Dynamics of a two-strain co-infection epidemic model with vaccination

Gang CHEN,Rui ZHANG

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2023, 58(10):  84-96.  doi:10.6040/j.issn.1671-9352.0.2022.543

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To explore the dynamics of co-infection of multiple strains in the same host population, a mathematical model of co-transmission dynamics of two strains after continuous inoculation with strain 1 vaccine is established and analyzed. Firstly, the sufficient conditions for the existence of four equilibrium points are obtained by calculating and analyzing the model. In addition to the disease-free equilibrium point and the two single endemic equilibrium points, the model also has an endemic equilibrium point where both strains 1 and 2 coexist. Secondly, Lyapunov stability theorem is used to prove that the disease-free equilibrium is globally stable when the basic reproduction number of two strains is less than 1. The invasion-reproduction number is introduced to determine the stability of the single-strain endemic equilibrium point. When the corresponding invasion reproduction number is less than 1, the endemic equilibrium point of the strain is locally stable. Then, using Castillo-Chavez and Song?s bifurcation theorem, it is proved that the model does not have backward bifurcation phenomenon, and then it is proved that the coexistence equilibrium point is locally asymptotically stable when the basic reproduction number of the two strains is greater than 1. Finally, the above conclusions are verified by numerical simulation.

Existence of traveling wave solutions for a diffusive predator-prey model

Hang ZHANG,Yujuan JIAO,Jinmiao YANG

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2023, 58(10):  97-105.  doi:10.6040/j.issn.1671-9352.0.2022.633

Abstract ( 147 )   HTML ( 3 )   PDF (2568KB) ( 124 )   Save

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In this paper, we discuss the existence of traveling wave solutions for a diffusive predator-prey model. Firstly, using linearization method, we prove non-existence of traveling wave solutions for the model with c < c^*. Secondly, we establish the existence of weak traveling wave solutions with c≥c^* by applying upper and lower solution method and Schauder's fixed point theorem. Moreover, utilizing Lyapunov function and LaSalle's invariance principle, we obtain that the weak traveling wave solutions for the model are traveling wave solutions under the suitable conditions. Finally, the numerical experiments support the validity of our theoretical results.

A reaction-diffusion model of avian influenza with imperfect vaccination

Mengjie HAN,Junli LIU

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2023, 58(10):  106-121.  doi:10.6040/j.issn.1671-9352.0.2022.666

Abstract ( 126 )   HTML ( 2 )   PDF (2489KB) ( 223 )   Save

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In this paper, a model of avian influenza with imperfect vaccination reaction-diffusion is established to study the transmission dynamics of avian influenza in birds considering the mobility of birds and environmental heterogeneity. The global existence of the solution of the model is proved, then the basic reproduction number of the model is calculated using the spectral radius of the next generation operator, and the threshold dynamics of the model are analyzed. We also consider the case where the vaccine has 100% preventive effect on birds, the explicit expressions of the basic reproduction number and the principal eigenvalue are given, extinction and persistence of viruses are investigated. Finally, numerical simulations are carried out to analyze the transmission dynamics of avian influenza, effective control strategies for the outbreaks of avian influenza are also discussed. It shows that increasing the coverage of bird vaccination, disinfecting the environment, removing the avian influenza virus in the environment, and reducing the migration of birds are very effective to control the spread of avian influenza.

Stability of a single population delayed reaction-diffusion model with Dirichlet boundary condition

Yonghua LI,Cunhua ZHANG

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2023, 58(10):  122-126.  doi:10.6040/j.issn.1671-9352.0.2023.131

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This paper studies the dynamics of a single population delayed reaction-diffusion model with Dirichlet boundary condition in a bounded domain. The existence and multiplicity of spatially nonhomogeneous steady-state solution is investigated by employing Lyapunov-Schmidt reduction method. Then, the stability of spatially nonhomogeneous steady-state solution is derived by analyzing the distribution of the eigenvalues.