Bifurcation Theory and Applications in Mathematical Biology

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My research area includes bifurcation theory and Hilbert's 16th problem for quadratic vector fields and application in mathematical biology. We hope to prove the finiteness part of the sweet Hilbert's 16th problem for quadratic vector fields, namely, to prove that there exists a natural number N such that any quadratic vector field in the plane has at most N limit cycles. I expect to prove that all the graphics with nilpotent point of elliptic or saddle type, degenerate graphics have finite cyclicity.West Nile virus, and other emerging and reemerging vector-borne diseaes are causing concerns to government, health officials and the public. By this study we will understand how the climate change has the impact on vector abundance and spreading of the diseases. This research will enable to create the early warning systems for prediction and control of vector-borne diseases in Canada.