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Colloquium, Spring 2005

Day: Tuesday May 31th Time: 4:00pm Place: BH 112 Title: Detection of limit cycles in Lienard systems Speaker: Bryan Hitchcock, WWU Limit cycles in dynamical systems represent a specific periodic solution in a phase plane diagram. In applications limit cycles mark periodic phenomena, such as in the modeling of the human heartbeat. In general finding the number of limit cycles for a specific dynamical system can be quite complicated and has connections to the unsolved Hilbert's 16th problem. In this talk we will look at certain dynamical systems known as Lienard systems, of which the van der Pol equation is a special case. In these systems a method developed by Melnikov gives us an analytical tool for detecting the existence and number of limit cycles. This method is further simplified by the assumptions made on the dynamical system. The method boils down to finding the roots of a polynomial in order to detect limit cycles. This talk will begin with a quick review of phase plane analysis of dynamical systems and bifurcations. Melnikov's method will then be outlined for detection of homoclinic bifurcation and limit cycles. Some theorems pertaining to location and number of limit cycles will be discussed followed by examples illustrating the method applied to Lienard systems. Cookies: In BH 300 at 3:30pm.