報(bào)告題目:Degenerate Bogdanov-Takens bifurcation of codimension 4 in Holling-Tanner model with harvesting
報(bào)告時(shí)間: 2022年6月22日(星期三), 20:00-20:40
報(bào)告地點(diǎn): 騰訊會(huì)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(bào)告人簡(jiǎn)介:華中師范大學(xué)教授、博士生導(dǎo)師。1999年、2002年分別本科、碩士畢業(yè)于華中師范大學(xué)數(shù)學(xué)系，2005年獲中國(guó)科學(xué)院數(shù)學(xué)與系統(tǒng)科學(xué)研究院數(shù)學(xué)所博士學(xué)位。主要從事常微分方程定性理論、分支理論及其應(yīng)用研究。在 JDE、SIAP、SIADS、JDDE、JMB、BMB 等期刊發(fā)表學(xué)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(diǎn)文章, 并被美國(guó)工業(yè)與應(yīng)用數(shù)學(xué)學(xué)會(huì)網(wǎng)站《SIAM News》專(zhuān)文報(bào)道。主持國(guó)家自然科學(xué)基金4項(xiàng)。曾獲湖北省自然科學(xué)獎(jiǎng)三等獎(jiǎng)。
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