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Riddled basins of attraction as seen on a two-dimensional slice of the infinite dimensional phase space

Riddled basins of attraction as seen on a two-dimensional slice of the infinite dimensional phase space

Extreme events in delay-coupled oscillators

Ph.D. Thesis

We studied a pair of identical FitzHugh-Nagumo oscillators which are diffusively coupled to each other by multiple time-delayed connections and identify regions in parameter space where extreme events can occur. The work is significant because it establishes that time-delayed couplings, which are ubiquitous in physical systems due to finite speed of transport of information and material, can cause extreme events even in absence of noise, external forcing, inhomogeneity of the coupled components and other factors previously known to induce extreme events.

Related Publications:


Synchronization in network of networks

collaboration with University of Bonn

Along with the research group of Prof. Dr. Klaus Lehnertz, we numerically studied the dynamics of diffusively coupled FitzHugh-Nagumo oscillators on a network of all-to-all-coupled, identical sub-networks. While for most of the parameter space the network exhibits the dynamical behaviors previously described for single uncoupled networks, we identify a region in parameter space where the interplay of the two different sets of coupling strengths allows for a richer dynamical behavior. Through computation of the Lyapunov exponents and constructing the bifurcation diagrams through slices of parameter space, we characterised the variety of qualitative dynamics observed and identified the regions of multistability.

Prediction of extreme events in a pair of oscillators (master) by a single oscillator (slave)

Prediction of extreme events in a pair of oscillators (master) by a single oscillator (slave)


Weak winner phase synchronization

collaboration within the group

While studying a model describing ecological food-chains, we found that if three such food-chains are coupled to each other diffusively in a chain, the system shows a novel type of synchronization where two weakly coupled food-chains do stay in phase synchrony while the two strongly coupled food-chains do not. We show that the such a counter-intuitive state (which we call ``weak winner'' phase synchrony) can be explained by anomalous phase synchronization which is a known phenomenon in nonlinear oscillators with shear (also known as `non-isochronicity'). We numerically demonstrate the existence of the weak winner phase synchronization state in simpler paradigmatic models like the Stuart-Landau and the Rössler oscillators. We also derive analytically sufficient conditions for the state to exist in Stuart-Landau oscillators.