Lei Zhang

Fudan University, Shanghai, Shanghai Shi, China

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Publications (8)10.73 Total impact

  • [show abstract] [hide abstract]
    ABSTRACT: In this paper, we present a theoretical analysis of processes of pattern formation that involves organisms distribution and their interaction of spatially distributed population with self as well as cross-diffusion in a Beddington–DeAngelis-type predator–prey model. The instability of the uniform equilibrium of the model is discussed, and the sufficient conditions for the instability with zero-flux boundary conditions are obtained. Furthermore, we present novel numerical evidence of time evolution of patterns controlled by self as well as cross-diffusion in the model, and find that the model dynamics exhibits a cross-diffusion controlled formation growth not only to stripes-spots, but also to hot/cold spots, stripes and wave pattern replication. This may enrich the pattern formation in cross-diffusive predator–prey model.
    Communications in Nonlinear Science and Numerical Simulation 01/2011; · 2.77 Impact Factor
  • [show abstract] [hide abstract]
    ABSTRACT: We present the temporal evolution of noise-controlled patterns in a spatially extended Gray–Scott model firstly. We show that the model exhibits a transition from stripe-spot growth to isolated spots, and also to spiral replication. Furthermore, we establish an extended Gray–Scott model with time-varying diffusivity, and find that the patterns exhibit transition from stripe-spot growth to stripe-spot or chaos replication. Additional studies reveal that with noise and time-varying diffusivity together, a new time-dependent pattern—a few of stripes oscillate in the “red” region—emerges, which hasn’t been reported before.
    Communications in Nonlinear Science and Numerical Simulation 01/2011; · 2.77 Impact Factor
  • [show abstract] [hide abstract]
    ABSTRACT: In this paper, we have presented Turing pattern selection in a ratio-dependent predator–prey model with zero-flux boundary conditions, for which we have given a general survey of the linear stability analysis and determined the condition of Turing instability, and derived amplitude equations for the excited modes. From the amplitude equations, the stability of patterns towards uniform and inhomogeneous perturbations is determined. Furthermore, we have presented novel numerical evidence of typical Turing patterns, and found that the model dynamics exhibits complex pattern replication: in the range μ1 < μ ≤ μ2, the steady state is the only stable solution of the model; in the range μ2 < μ ≤ μ4, on increasing the control parameter μ, the sequence Hπ-hexagons -hexagon–stripe mixture stripes -hexagon–stripe mixture -hexagons is observed; and when μ > μ4, an H0-hexagon–stripe mixture pattern emerges. This may enrich the pattern formation in a diffusive system.
    Journal of Statistical Mechanics Theory and Experiment 11/2010; 2010(11):P11036. · 1.87 Impact Factor
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    ABSTRACT: In this paper, we investigate the spatial pattern formation of a predator–prey system with prey-dependent functional response Ivlev-type and reaction-diffusion. The Hopf bifurcation of the model is discussed, and the sufficient conditions for the Turing instability with zero-flux boundary conditions are obtained. Based on this, we perform the spiral and the chaotic spiral patterns via numerical simulation, i.e., the evolution process of the system with the initial conditions which was small amplitude random perturbation around the steady state. For the sake of learning the pattern formation of the model further, we perform three categories of unsymmetric initial condition, and find that with these special initial conditions the system can emerge not only spiral pattern but also target pattern and so on, and the effect of these special conditions on the formation of spatial patterns is less and less with more and more iterations but the effect does not decay forever. This indicates that for prey-dependent type predator–prey system, pattern formations do depend on the initial conditions, while for predator-dependent type they do not.
    Ecological Modelling 01/2010; 221:131-140. · 2.07 Impact Factor
  • Lei Zhang, Wenjuan Wang, Yakui Xue
    [show abstract] [hide abstract]
    ABSTRACT: In this paper, we investigate the emergence of a predator–prey system with Michaelis–Menten-type predator–prey systems with reaction–diffusion and constant harvest rate. We derive the conditions for Hopf and Turing bifurcation on the spatial domain. The results of spatial pattern analysis, via numerical simulations, typical spatial pattern formation is isolated groups, i.e., stripe-like, patch-like and so on. Our results show that modeling by reaction–diffusion equations is an appropriate tool for investigating fundamental mechanisms of complex spatiotemporal dynamics. It will be useful for studying the dynamic complexity of ecosystems.
    Chaos Solitons & Fractals 01/2009; · 1.25 Impact Factor
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    ABSTRACT: In this paper, we focus on a spatial Holling-type IV predator-prey model which contains some important factors, such as diffusion, noise (random fluctuations) and external periodic forcing. By a brief stability and bifurcation analysis, we arrive at the Hopf and Turing bifurcation surface and derive the symbolic conditions for Hopf and Turing bifurcation in the spatial domain. Based on the stability and bifurcation analysis, we obtain spiral pattern formation via numerical simulation. Additionally, we study the model with colored noise and external periodic forcing. From the numerical results, we know that noise or external periodic forcing can induce instability and enhance the oscillation of the species, and resonant response. Our results show that modeling by reaction-diffusion equations is an appropriate tool for investigating fundamental mechanisms of complex spatiotemporal dynamics.
    02/2008;
  • Source
    [show abstract] [hide abstract]
    ABSTRACT: In this paper, we investigate the emergence of a predator-prey model with Beddington-DeAngelis-type functional response and reaction-diffusion. We derive the conditions for Hopf and Turing bifurcation on the spatial domain. Based on the stability and bifurcation analysis, we give the spatial pattern formation via numerical simulation, i.e., the evolution process of the model near the coexistence equilibrium point. We find that for the model we consider, pure Turing instability gives birth to the spotted pattern, pure Hopf instability gives birth to the spiral wave pattern, and both Hopf and Turing instability give birth to stripe-like pattern. Our results show that reaction-diffusion model is an appropriate tool for investigating fundamental mechanism of complex spatiotemporal dynamics. It will be useful for studying the dynamic complexity of ecosystems.
    02/2008;
  • [show abstract] [hide abstract]
    ABSTRACT: This paper presents a new simplified adaptive channel prediction scheme for MIMO-OFDM system. It is based on the conjugate gradient (CG) algorithm. This simplification also uses Alamouti's STBC code which leads to a simple decoding process. Compared with the traditional RLS algorithm, CG performances better in the decision-directed demodulation mode. And this scheme is also designed to have the capability to restrain the noise and it causes a better prediction result.
    01/2008;

Publication Stats

21 Citations
10.73 Total Impact Points

Institutions

  • 2011
    • Fudan University
      • School of Mathematical Sciences
      Shanghai, Shanghai Shi, China
  • 2010–2011
    • East China Normal University
      • Department of Computer Science & Technology
      Shanghai, Shanghai Shi, China
  • 2009
    • Chengdu University of Technology
      Hua-yang, Sichuan, China
    • North University of China
      Yangkü, Shanxi Sheng, China
  • 2008
    • Wenzhou University
      Yung-chia, Zhejiang Sheng, China