Kiran M. Kolwankar

STDP-driven networks and the C. elegans neuronal network

We study the dynamics of the structure of a formal neural network wherein the strengths of the synapses are governed by spike-timing-dependent plasticity (STDP). For properly chosen input signals, there exists a steady state with a residual network. We compare the motif profile of such a network with that of a real neural network of C. elegans and identify robust qualitative similarities. In particular, our extensive numerical simulations show that this STDP-driven resulting network is robust under variations of the model parameters.

Evolution of network structure by temporal learning

We study the effect of learning dynamics on network topology. A network of discrete dynamical systems is considered for this purpose and the coupling strengths are made to evolve according to a temporal learning rule that is based on the paradigm of spike-time-dependent plasticity. This incorporates necessary competition between different edges. The final network we obtain is robust and has a broad degree distribution.

GLOBAL ANALYSIS OF SYNCHRONIZATION IN COUPLED MAPS

We introduce a new method for determining the global stability of synchronization in systems of coupled identical maps. The method is based on the study of invariant measures. Besides the simplest nontrivial example, namely two symmetrically coupled tent maps, we also treat the case of two asymmetrically coupled tent maps as well as a globally coupled network. Our main result is the identification of the precise value of the coupling parameter where the synchronizing and desynchronizing transitions take place.

Fractal Stationary Density in Coupled Maps

We study the invariant measure or the stationary density of a coupled discrete dynamical system as a function of the coupling parameter e (0 < e < 1/4). The dynamical system considered is chaotic and unsynchronized for this range of parameter values. We find that the stationary density, restricted on the synchronization manifold, is a fractal function. We find the lower bound on the fractal dimension of the graph of this function and show that it changes continuously with the coupling parameter.

Effect of heat source on the growth of dendritic drying patterns

Shining a tightly-focussed but low-powered laser beam on an absorber dispersed in a biological fluid gives rise to spectacular growth of dendritic patterns. These result from localized drying of the fluid because of efficient absorption and conduction of optical energy by the absorber. We have carried out experiments in several biologically relevant fluids and have analysed patterns generated by different types of absorbers. We observe that the growth velocity of branches in the dendritic patterns can decrease below the value expected for natural drying.