20 Result(s)
within
Mathematics
Junjie Wei
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Article
Hopf Bifurcation of a Delayed Single Population Model with Patch Structure
In this paper, we show the existence of a Hopf bifurcation in a delayed single population model with patch structure. The effect of the dispersal rate on the Hopf bifurcation is considered. Especially, if each...
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Article
Perceptive movement of susceptible individuals with memory
The perception of susceptible individuals naturally lowers the transmission probability of an infectious disease but has been often ignored. In this paper, we formulate and analyze a diffusive SIS epidemic mod...
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Article
Bifurcation analysis for a single population model with advection
In this paper, the dynamics of a single population model with a general growth function is investigated in an advective environment. We show the existence of a nonconstant positive steady state, and give suffi...
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Article
Bifurcation Analysis for a Delayed Diffusive Logistic Population Model in the Advective Heterogeneous Environment
In this paper, we investigate a delayed reaction–diffusion–advection equation, which models the population dynamics in the advective heterogeneous environment. The existence of the nonconstant positive steady ...
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Article
Stationary Pattern of a Reaction–Diffusion Mussel–Algae Model
In this paper, we consider a reaction–diffusion mussel–algae model with state-dependent mussel mortality. This mortality involves a positive feedback term resulting from the reduction of dislodgment and predat...
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Article
Double Hopf Bifurcation in Delayed reaction–diffusion Systems
Double Hopf bifurcation analysis can be used to reveal some complicated dynamical behavior in a dynamical system, such as the existence or coexistence of periodic orbits, quasi-periodic orbits, or even chaos. ...
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Article
Dynamics of a Diffusive Predator–Prey Model: The Effect of Conversion Rate
A general diffusive predator–prey model is investigated in this paper. We prove the global attractivity of constant equilibria when the conversion rate is small, and the non-existence of non-constant positive ...
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Article
The Effect of Delay on A Diffusive Predator–Prey System with Modified Leslie–Gower Functional Response
In this paper, a delayed diffusive modified Leslie–Gower-type predator–prey model with Beddington–DeAngelis functional response subject to Neumann boundary condition is considered. The stability/instability of...
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Article
Open AccessAnalysis of dynamics in an eco-epidemiological model with stage structure
This paper is devoted to the study of an eco-epidemiological model with stage structure in the predator and disease in the prey. To begin with, the positivity and boundedness of the solutions are obtained. Thi...
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Article
Minimal Model of Plankton Systems Revisited with Spatial Diffusion and Maturation Delay
This study revisits the minimal model for a plankton ecosystem proposed by Scheffer with spatial diffusion of plankton and the delay of the maturation period of herbivorous zooplankton. It deepens our understa...
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Article
Open AccessStability and bifurcation analysis in a viral infection model with delays
In this paper, a class of virus infection models with CTLs response is considered. We incorporate an immune delay and two intracellular delays into the virus infection model. It is found that only incorporatin...
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Article
Global Hopf Bifurcation Analysis of a Nicholson’s Blowflies Equation of Neutral Type
We investigate Hopf bifurcations in a delayed Nicholson’s blowflies equation of neutral type, derived from the Gurtin–MacCamy model. A key parameter that determines the direction of the Hopf bifurcation and th...
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Article
Time Delay-Induced Instabilities and Hopf Bifurcations in General Reaction–Diffusion Systems
The distribution of the roots of a second order transcendental polynomial is analyzed, and it is used for solving the purely imaginary eigenvalue of a transcendental characteristic equation with two transcende...
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Chapter
Global Hopf Bifurcation Analysis of a Neuron Network Model with Time Delays
For a two-neuron network with self-connection and time delays, we carry out stability and bifurcation analysis. We establish that a Hopf bifurcation occurs when the total delay passes a sequence of critical va...
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Article
Hopf Bifurcation in a Diffusive Logistic Equation with Mixed Delayed and Instantaneous Density Dependence
A diffusive logistic equation with mixed delayed and instantaneous density dependence and Dirichlet boundary condition is considered. The stability of the unique positive steady state solution and the occurren...
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Article
Open AccessBifurcation analysis of a diffusive model of pioneer and climax species interaction
A diffusive model of pioneer and climax species interaction is considered. We perform a detailed Hopf bifurcation analysis to the model, and derive conditions for determining the bifurcation direction and the ...
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Article
Periodicity and synchronization in blood-stage malaria infection
Malaria fever is highly periodic and is associated with the parasite replication cycles in red blood cells. The existence of periodicity in malaria infection demonstrates that parasite replication in different...
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Article
Predator–prey system with strong Allee effect in prey
Global bifurcation analysis of a class of general predator–prey models with a strong Allee effect in prey population is given in details. We show the existence of a point-to-point heteroclinic orbit loop, cons...
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Article
Singularity Analysis on a Planar System with Multiple Delays
A planar model with multiple delays is studied. The singularities of the model and the corresponding bifurcations are investigated by using the standard dynamical results, center manifold theory and normal for...
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Article
Stability Switches and Hopf Bifurcations in a Pair of Delay-Coupled Oscillators
In this paper, we consider a pair of delay-coupled limit-cycle oscillators. Regarding the arithmetical average of two delays as a parameter, we investigate the effect of time delays on its dynamics. We show th...
