Mathematical Biology Seminar Kei-ichi Ueda RIMS, Kyoto University Wednesday Jan. 23, 2008 3:05pm in LCB 215 "Pulse dynamics in heterogeneous media " Abstract: One of the fundamental issues in reaction-diffusion systems is to clarify input-output relation when traveling pulses encounter heterogeneous media. In the Gray-Scott model, a variety of types of patterns have been observed in bump or periodic type heterogeneous media. We focus on the dynamics of pulses in heterogeneous media when the associated parameters are close to pitchfork and saddle-node bifurcations. In order to elucidate the underlying mechanism causing variety of dynamics by reducing the PDE dynamics to finite dimensional equations. If time allows, I will talk about dynamic behavior of the frontal tip of the plasmodium of the true slime mold in heterogeneous media. The plasmodium migrating in a narrow lane shows penetration, rebound and splitting dynamics when it encounters the presence of chemical repellent, quinine. I will discuss how the origin of the three different outputs could be reduced to the hidden instabilities of internal dynamics of the tip.