Title: Extinction of species and extreme events                                        

AbstractMore than 99 % species that ever existed on the earth are now extinct. Extinction of the species on a global scale is a puzzle due to the 'rescue effect'. According to the rescue effect, a species under an external threat may survive in some isolated locations and then can lead to the revival of the species. We show using a general model that under a common external forcing, the species first undergoes spatial synchronization and then extinction. This is because the competition term in the population dynamics reduces the synchronization time scale but not the extinction time scale. Thus the populations do not survive in isolated locations and extinction takes place almost simultaneously in all the locations. This avoids the rescue effect.

Second part of the talk will cover extreme events on networks. Extreme events are very common in nature and many times they are associated with some calamities such as typhoons, earthquakes, floods etc. In many cases, there is some underlying network on which the extreme events take place, e.g. traffic jams on transport network, power black-outs on electrical grids, floods on river network etc. We study extreme events on complex networks using the random walk model. We find that the nodes with smaller number of links are more prone to extreme events than the ones with larger number of links.

Our study brings out the importance of fluctuations of the internal dynamics of the network in extreme events.