Mathematical Physics Seminar: Stability of Synchronised Chaos and Extinction of Species

Professor Govindan Rangarajan, Department of Mathematics, Indian Institute of Science, Bangalore

Monday 07 May 2012, 1400-1500
Frankland Colloquium Room

We will start by considering the synchronized state in a coupled system of oscillators/maps. Stability bounds for the synchronized state are obtained in terms of the coupling coefficients. We then link the problem of synchronization to the problem of global extinction of species. More than 99% of the species that ever existed on the surface of the Earth are now extinct and their extinction on a global scale has been a puzzle. One may think that a species under an external threat may survive in some isolated locations leading to the revival of the species. Using a general model we show that, under a common external forcing, the species with a quadratic saturation term first undergoes spatial synchronization and then extinction. The effect can be observed even when the external forcing acts only on some locations provided the dynamics contains a synchronizing term. Absence of the quadratic saturation term can help the species to avoid extinction.