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coexistence state of competition model in chemostat

Progress in Natural Science:Materials International 1998年第6期 110-114页

作者：吴建华 Department of Mathematics Shaanxi Normal University Xi’an 710062 Xidian University Xi’an 710071 China

The structure of the non-negative steady-state solutions of a system of reaction diffusion equations arising in the chemostat is investigated. The ranges of parameters for the coexistence of steady-state solutions are given by the theorem of global bifurcation and maximal principle. The global structure of the coexistence solutions is completely obtained. Partial stability is also established.

关键词： global bifurcation coexistence state reaction diffusion equation stability.

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coexistence of noise-like pulse and dark pulse in an Er/Yb co-doped fiber laser

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Chinese Optics Letters 2024年第5期22卷 68-74页

作者：李婧王春灿王鹏 Key Laboratory of All Optical Network and Advanced Telecommunication Network Ministry of EducationInstitute of Lightwave TechnologyBeijing Jiaotong UniversityBeijing 100044China

The coexistence of a noise-like pulse(NLP)and a dark pulse was experimentally demonstrated in a net-anomalous dispersion Er/Yb co-doped fiber(EYDF)laser,for the first time,to our *** cavity was mode-locked by nonlinear polarization rotation(NPR)***,a Sagnac loop with a section of polarization-maintaining fiber(PMF)was used as a comb filter to enable multiwavelength pulse *** the PMF length was 0.3 m,an asymmetric two-peak spectrum with central wavelengths of 1565.3 and 1594.2 nm was obtained by adjusting polarization controllers(PCs).It is a composite state of NLP and dark pulse due to the cross-phase modulation between the two different wavelength components along orthogonal polarization *** two pulses are synchronized with a repetition rate of 7.53 *** adjusting the PC in the Sagnac loop,the spectral ranges of NLPs and dark pulses can be tuned from 1560 to 1577.8 nm and from 1581.8 to 1605.4 nm,*** addition,the pulse characteristics were investigated by incorporating the PMF with different lengths,where the coexistence patterns can be generated when the PMF lengths were 0.2 and 0.3 m.A longer PMF can lead to a narrowband comb filtering,which causes a larger loss and is not favorable for stable operation of the coexistence *** fiber laser demonstrates an interesting operation regime and has significant potential for numerous practical applications.

关键词： coexistence state mode-locked fiber laser Sagnac loop tunable wavelength

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FURTHER IN VESTIGATION OF THE VOLTERRA-LOTKA COMPETITION MODEL WITH DIFFUSION

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Applied Mathematics(A Journal of Chinese Universities) 1998年第2期13卷 135-140页

作者： HUANG JIANJUN Department of Mathematics Fuzhou University Fuzhou

In this paper, the existence of coexistence states in the Voterra Lotka competition model under Dirichlet boundary conditions is the major concern. Attention will be focused on the logistic equation. With a comparison theorem an inequality satisfied by the solution of logistic equation is established. Some improved sufficient conditions for the existence of coexistence states are obtained.

关键词： Competition system Logistic equation coexistence state

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An Elliptic Nonlinear System of Two Functions with Application

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Journal of Partial Differential Equations 2023年第2期36卷 122-146页

作者： KANG Joon Hyuk ROBERTSON Timothy Department of Mathematics Andrews UniversityBerrien Springs MI.49104-0350U.S.A Department of Mathematics University of TennesseeKnoxville TN.37996-1320U.S.A

The purpose of this paper is to give a sufficient conditions for the existence and uniqueness of positive solutions to a rather general type of elliptic system of the Dirichlet problem on a bounded domain Ω in R^(n).Also considered are the effects of perturbations on the coexistence state and *** techniques used in this paper are super-sub solutions method,eigenvalues of operators,maximum principles,spectrum estimates,inverse function theory,and general elliptic *** arguments also rely on some detailed properties for the solution of logistic *** results yield an algebraically computable criterion for the positive coexistence of competing species of animals in many biological models.

关键词： Competition system coexistence state

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