Supervisor: Prof. Dr. Ulrike Feudel
Due to their catastrophic and unforeseen impact on a large class of natural systems, studies investigating their characteristics, generating mechanisms, prediction and prevention techniques have increased manifold in recent times. These areas also form the major motivation of my PhD thesis where new mechanisms of generation of such events and their prediction have been presented in addition to new rich and interesting dynamical properties.
Stability & Phase Space Structure of Networks of LIF Neurons
Supervisor: Dr. Raoul-Martin Memmesheimer
In this project we computed and analysed the complete Lyapunov spectra of networks of normal and anomalous dissipation LIF neuron and studied the effect of concavity and convexity of potential rise functions of neurons on the overall stability of the neural network.
Supervisor: Prof. Soumitro Banerjee
There are many systems in nature that behave differently in different situations. They are generally represented by maps that are separately defined in different regions in the phase space and are hence non-smooth across a boundary. Due to the presence of the boundary, many novel phenomena like a stable periodic orbit many a direct transition to chaos is seen. In this project, we investigate one such phenomena, called the dangerous bifurcation, in which the basin of attraction of a stable orbit shrinks to zero at the bifurcation point. Hence, even though a stable orbit remains stable across the parameter region, all trajectories around the orbit diverge away at the point of point of bifurcation. We try to develop a generic theory for the bifurcation and characterize it as far as possible.
Synchronization of Kuramoto Oscillators
Supervisor: Prof. Ravindra E. Amritkar
We studied the behaviour of oscillators under Kuramoto Model in various kinds of networks. We then focussed on the ring network of the oscillators and devised new ways of controlling the synchronization frequency of based on the symmetry of the natural frequency distribution.
Stability of Networks of Rapid Theta Neurons
Supervisor: Prof. Dr. Fred Wolf
We investigated the dynamics of Erdós Rényi networks of Rapid Theta neurons for low rapidness. We analyse the emergence of synchrony in the spiking frequency and study the dependence of Lyapunov stability, entropy production and the dimensionality of attractor on various properties of the network.
Unfolded Protein Response: An Improved Mathematical Model
Supervisor: Dr. Pranay Goel
Here we analysed the response of the protein folding machinery of the endoplasmic reticulum under the conditions of high protein concentrations. Using the model proposed by Dr. Santiago Schnell (in his paper ‘A Model of the Unfolded Protein Response: Pancreatic β-Cell as a Case Study’) as a base, we improve the model by incorporating the effect of PERK on the model.