報(bào)告題目:Existence and uniqueness of periodic orbits in a discrete model on Wolbachia infection frequency
報(bào)告時(shí)間: 2022年6月22日(星期三), 20:50-21:30
報(bào)告地點(diǎn): 騰訊會(huì)議 846 210 770
內(nèi)容摘要: This talk consider a discrete model on Wolbachia infection frequency. In the model, a periodic and impulsive release strategy is assumed, where infected males are released during the first N generations with the release ratio a and the release is terminated from N+1-th generation to T-th generation. We find a release ratio threshold denoted by b and prove the existence of periodic solutions for the model when 0<a<b. For the special case when N=1 and T=2 we prove that the model has a unique periodic solution which is unstable when 0<a<b. While a>b, no periodic phenomenon occurs and the Wolbachia fixation equilibrium is globally asymptotically stable. Numerical simulations are also provided to illustrate our theoretical results. One main contribution of this work is to offer a new method to determine the exact number of periodic orbits to discrete models. However, for the general case, the uniqueness of the periodic solution is still pending. This is a joint work with Prof Jianshe Yu in Guangzhou University.
報(bào)告人簡(jiǎn)介:鄭波，博士，教授，博士生導(dǎo)師。主要從事常微分方程、泛函微分方程及生物數(shù)學(xué)模型的理論與應(yīng)用研究，在《Nature》、《SIAM Journal of Applied Mathematics》、《Journal of Mathematical Biology》、《中國科學(xué)》、《Journal of Differential Equations》、《Journal of Dynamics and Differential Equations》、《Journal of Theoretical Biology》、《Theoretical Population Biology》等國際國內(nèi)重要刊物上發(fā)表論文30余篇。先后主持國家自然科學(xué)基金4項(xiàng)、廣州市教育局3項(xiàng)，2014年入選廣東省高校優(yōu)秀青年教師培育對(duì)象，是教育部創(chuàng)新團(tuán)隊(duì)“泛函微分方程及相關(guān)問題”的骨干成員。 獲得首屆秦元?jiǎng)浊嗄陻?shù)學(xué)獎(jiǎng)。
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