Scaling and synchronization in a ring of diffusively coupled nonlinear oscillators

Synchronization of nearly identical dynamical systems: Size instability

We study the generalized synchronization and its stability using the master stability function (MSF) in a network of coupled nearly identical dynamical systems. We extend the MSF approach for the case of degenerate eigenvalues of the coupling matrix. Using the MSF we study the size instability in star and ring networks for coupled nearly identical dynamical systems. In the star network of coupled Rössler systems we show that the critical size beyond which synchronization is unstable can be increased by having a larger frequency for the central node of the star. For the ring network we show that the critical size is not significantly affected by parameter variations. The results are verified by explicit numerical calculations.

Live visualizations of single isolated tubulin protein self-assembly via tunneling current: effect of electromagnetic pumping during spontaneous growth of microtubule

As we bring tubulin protein molecules one by one into the vicinity, they self-assemble and entire event we capture live via quantum tunneling. We observe how these molecules form a linear chain and then chains self-assemble into 2D sheet, an essential for microtubule, —fundamental nano-tube in a cellular life form. Even without using GTP, or any chemical reaction, but applying particular ac signal using specially designed antenna around atomic sharp tip we could carry out the self-assembly, however, if there is no electromagnetic pumping, no self-assembly is observed. In order to verify this atomic scale observation, we have built an artificial cell-like environment with nano-scale engineering and repeated spontaneous growth of tubulin protein to its complex with and without electromagnetic signal. We used 64 combinations of plant, animal and fungi tubulins and several doping molecules used as drug, and repeatedly observed that the long reported common frequency region where protein folds mechanically and its structures vibrate electromagnetically. Under pumping, the growth process exhibits a unique organized behavior unprecedented otherwise. Thus, “common frequency point” is proposed as a tool to regulate protein complex related diseases in the future.

Synchronization in simple network motifs with negligible correlation and mutual information measures

Can different or even identical coupled oscillators be completely uncorrelated and still be synchronized? What can be concluded from the absence of correlations or even mutual information in networks of dynamical elements about their connectivity? These are fundamental and far-reaching questions arising in many complex systems. In this Letter, we address these two questions and demonstrate in simple and generic network motifs that synchronized behavior in the generalized sense can be realized and constructed such that no correlations and even negligible mutual information remain. Our findings raise new questions, in particular, whether and to what extent indirect connections are being underestimated, since the related collective behavior and even synchronization are less likely to be detected.