報告題目:Degenerate Bogdanov-Takens bifurcation of codimension 4 in Holling-Tanner model with harvesting
報告時間: 2022年6月22日(星期三), 20:00-20:40
報告地點: 騰訊會議 846 210 770
內(nèi)容摘要:In this talk, we revisit the Holling-Tanner model with constant-yield prey harvesting. It is shown that the highest codimension of a nilpotent cusp is 4, and the model can undergo degenerate Bogdanov-Takens bifurcation of codimension 4. Moreover, when the model has a center-type equilibrium, we show that it is a weak focus with order at least 3 and at most 4, and the model can exhibit Hopf bifurcation of codimension 3. Some algebraic methods including resultant elimination and pseudo-division are used to solve the semi-algebraic varieties of normal form coefficients or focal values. Our results indicate that constant-yield prey harvesting can cause not only richer dynamics and bifurcations, but also the coextinction of both populations with some positive initial densities.
報告人簡介:華中師范大學教授、博士生導師。1999年、2002年分別本科、碩士畢業(yè)于華中師范大學數(shù)學系，2005年獲中國科學院數(shù)學與系統(tǒng)科學研究院數(shù)學所博士學位。主要從事常微分方程定性理論、分支理論及其應用研究。在 JDE、SIAP、SIADS、JDDE、JMB、BMB 等期刊發(fā)表學術(shù)論文四十余篇。其中發(fā)表在 SIADS (2019) 的文章被選為封面亮點文章, 并被美國工業(yè)與應用數(shù)學學會網(wǎng)站《SIAM News》專文報道。主持國家自然科學基金4項。曾獲湖北省自然科學獎三等獎。
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