Collective dynamics of networks of nonlinear systems

Collective dynamics of networks of nonlinear systems Examples: information processing in networks of neurons, simultaneous flashing of fireflies, synchrony in powergrids, . . .

Challenges include the development of systematic tools for studying stability, robustness and bifurcation in such dynamical networks Possible MSc projects I

Predicting patterns of oscillation in networks of model neurons

I

Harmonic balancing methods for neural mass models

Dynamics and control of biochemical circuits Building biochemical I

actuators

I

sensors

I

oscillators

for creation of smart drugs

exonuclease

βi

Activator Product

T3

Inhibitor

T5

Template polymerase

γ

T1

α

β

T4

nickase pol. SD

T2

T6

αi building block (DNA circuit)

Toggle switch (sensor + actuator)

δ

Dynamics and control of biochemical circuits

( cont’d)

The dynamics of these DNA circuits are poorly understood. There is a need for I

methods for systematic and robust design of functional circuits

I

model reduction procedures (reduction of number of parameters may simplify design)

I

parameter estimation procedures (for model validation)

I

...

Possible MSc projects I

Design of adaptive observers for a DNA circuit

I

Reduced order modeling of a toggle-switch