Hongjian Guo

Hongjian Guo
Xinyang Normal University · College of Mathematics and Information Sicence

About

32
Publications
1,131
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386
Citations
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July 1994 - present
Xinyang Normal University
Position
  • Professor (Associate)

Publications

Publications (32)
Article
Full-text available
In this paper, a pest management predator–prey model with weak Allee effect on predator and state feedback impulsive control on prey is introduced and analysed, where the yield of predator released and intensity of pesticide sprayed are assumed to be linearly dependent on the selected pest control level. For the proposed model, the existence and st...
Article
Full-text available
Agricultural pests are great threat for agricultural production, and the development of effective pest control methods is becoming an interesting topic and attracts great attentions. In this work, an integrated pest management model with Leslie–Gower type and ratio-dependent functional response is investigated, and the sufficient conditions for the...
Article
Considering the fact that the production and provision of some vaccines are ordered and governed by the government according to the history data of disease, a kind of SIR model with constant vaccination rate and impulsive state feedback control is presented. The dynamical properties of semi-continuous three-dimensional SIR system can be obtained by...
Article
a r t i c l e i n f o MSC: 34C05 92D25 Keywords: Antibiotic therapy Wild-type and resistant bacteria Erythromycin–Vancomycin Impulsive input Basic reproduction ratio Persistence a b s t r a c t A nosocomial-pathogens-infections model with impulsive antibiotics treatment on multiple bacteria and time-dependent drug efficacy is proposed in this paper...
Article
On the basis of the ideas of non-traditional biomanipulation control in fresh water body, a kind of nutrient–algae fish model is presented to investigate the effects of constant releasing fish on the nutrient and the algae. The threshold conditions for the extinction of the algae are obtained by discussing the stability of boundary equilibrium. The...
Article
A kind of consumer-resource system is proposed to describe the bidirectional interactions of the algae and the fish in an eutrophic water body. The dynamical properties of the proposed continuous system are given. For the bistable case, an impulsive semidynamical system with state feedback control, which depends on the biomass of the algae, is form...
Article
A kind of cylindrical dynamic system with impulsive state feedback control is formulated and investigated. Based on the qualitative properties of the corresponding continuous system, the existence of order-k(k∈Z+) periodic solutions of the cylindrical dynamic system with impulsive state feedback control is discussed on the cylinder with perimeter 2...
Article
A korean pine forest model with impulsive thinning measure is presented by using impulsive state feedback system to investigate the periodicity of the regeneration process of the forest. Based on the qualitative properties of the corresponding continuous system, the existences of order-1 periodic solutions are discussed. If the positive equilibrium...
Article
We propose two novel mathematical models with impulsive injection of insulin or its analogues for type 1 and type 2 diabetes mellitus. One model incorporates the periodic impulsive injection of insulin. We analytically show the existence and uniqueness of a positive globally asymptotically stable periodic solution for type 1 diabetes, which implies...
Article
According to the initial density of a single species with Allee effect and corresponding management strategy, three kinds of mathematical models are presented to describe the evolutionary process of the species by impulsive differential equations. When the initial density of the species is larger than economic injury level (EIL) (or economical thre...
Article
Two kinds of time-limited pest control models of single-pest with stage-structure, which can be described by the boundary value problem of ordinary differential equation and impulsive differential equation, are presented according to the ways of artificial control (continuous control and impulsive control). The conditions under which the correspond...
Article
A turbidostat is an apparatus with feedback control system used to continuously culturing microorganisms. The dilution rate of the turbidostat can be regulated by the control system when the concentration of microorganism, detected by photoelectricity system or other devices, reaches a preset value. Based on the design ideas of the turbidostat, a d...
Article
A kind of time-limited control model on a competition system with impulsive harvest, described by impulsive differential equation with the initial and boundary value problem, is presented. The existence of solution of the model, corresponding to the feasibility of the short-term control, is discussed. By the comparison principle, the conditions und...
Article
A turbidostat is an apparatus used to continuously culturing microorganisms. The concentration of the microorganism in the turbidostat can be controlled by the photoelectricity system or other devices. When the concentration of the microorganism is lower than a critical level, the dilution rate keeps constant. Once the concentration reaches the cri...
Article
A kind of species control model concerning impulsive releasing pathogen and infective predator is presented. By using the Floquet theory and comparison theorem of impulsive differential equation, the extinction and permanence of system are discussed and the corresponding conditions are obtained, respectively. Finally, the practical meanings of thos...
Article
In this paper, we develop a mathematical model concerning a chemostat with impulsive state feedback control to investigate the periodicity of bioprocess. By the existence criteria of periodic solution of a general planar impulsive autonomous system, the conditions under which the model has a periodic solution of order one are obtained. Furthermore,...
Article
A kind of predator–prey system with distributed time delay and impulsive harvest is firstly presented and then the effects of impulsive harvest on the system are discussed by means of chain transform. By using the Floquet’s theory and the comparison theorem of impulsive differential equation, the thresholds between permanence and extinction of each...
Article
A kind of time-limited pest control of a Lotka–Volterra model with impulsive harvest, described by the initial and boundary value problem of impulsive differential equation, is presented. The aim of pest control can be achieved if the model has a solution, otherwise the aim cannot be achieved. By the comparison principle, the conditions under which...
Article
A kind of one-prey two-predator system with Ivlev's and Beddington–DeAngelis' functional response and impulsive release at fixed moments is presented. It is shown that the system has a prey-free periodic solution. By using the Floquet theory and small amplitude perturbation skills, it is proved that the prey-free periodic solution of the system is...
Article
Two kinds of time-limited management strategies of a single-species with Allee effect, described by the impulsive differential equation with initial and boundary value conditions, are presented according to the initial density of the species. By means of the comparison principle and the methods of upper and lower solutions, boundary value problems...
Article
In this paper, we consider a predator-prey system with stage structure. The populations have two stages, an immature stage and a mature stage, the age to maturity is represented by a time delay, which leads to systems of retarded functional differential equations. We obtain the conditions for global asymptotic stability of two nonnegative equilibri...
Article
An impulsive predator–prey system with modified Leslie–Gower and Holling-type II schemes is presented. By using the Floquet theory of impulsive equation and small amplitude perturbation method, the globally asymptotical stability of prey-free positive periodic solution and the permanence of system are discussed. The corresponding threshold conditio...
Article
A kind of predator-prey systems of Holling type II and interaction perturbations with impulsive effects is presented. By using the Floquet theory and small amplitude perturbations, the local asymptotic stability of prey-eradication periodic solutions and the permanence of the system are discussed, and the corresponding threshold conditions are give...
Article
Full-text available
In this paper, a kind of pest-predator model with impulsive effect and infinite delay is considered by the method of chain transform. By using Floquet's theorem, it is shown that there exists a globally asymptotically stable periodic pest eradication solution when the impulsive period is less than or equal to some critical value which is a directly...
Article
A simple model for a chemostat with predator-prey species and periodically pulsed substrate is proposed. Exact periodic solutions with positive concentrations of substrate and prey (predator) are obtained, the stability of these solutions is analysed. When the period exceeds a critical value, the periodic solution loses its stability.

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