COLÓQUIO MAP e MINICURSO
“Dynamics on Networks and Applications”
Two lectures: June, 23 (Friday) - first lecture: 10:00 - 11:30 second lecture: 16:00 - 17:30
Conferencista: Prof. Martin Golubitsky (Ohio State University)
Dia: 23 de junho, quarta-feira, Auditório Antonio Gilioli, Sala 247/262, Bloco A, IMEUSP, das 10 às 11h30 e das 16h às 17h30, Café às 9h30 e às 15h30, na sala 265 A (Chefia do MAP).
Transmissão online: http://www.ime.usp.br/comunicacao/eventos/cat.listevents/
Resumo da palestra:
These lectures will discuss some of the ways in which the dynamics of coupled systems of differential equations and their bifurcations differ from general systems of differential equations. In this theory a network is a graph (also called the network architecture) where nodes correspond to state variables and arrows to coupling (who is talking to whom). What distinguishes network dynamics from that of systems of ODEs is the fact that one wants to keep track of the nodal dynamics for each node. There is a natural way to associate to each graph a space of admissible systems of differential equations; the mathematical questions that are asked are: How does network architecture affect the generic dynamics and the bifurcations within the class of admissible systems and what are the invariants of these systems. For example, synchrony (the time-evolution of two nodes being identical) and phase-shift synchrony (two nodes in a periodic solution are identical up to a phase-shift) occur naturally in networks and are products of network architecture. Network symmetry also plays an important role. These lectures will discuss applications to gaits of four-legged animals (quadrupedal locomotor central pattern generators), binocular rivalry (how does the brain deal with contradictory information), and homeostasis (a property of a stable equilibrium that remains almost constant as an input parameter is varied).
APOIO: FAPESP-OSU através do projeto de colaboração "Geometry and Dynamics Between Ohio and São Paulo" (Processo FAPESP: 2015/50315-3).
