Shrimali, Manish Dev

We study the dynamics of oscillators that are coupled in relay; namely, through an intermediary oscillator. From previous studies it is known that the oscillators show a transition from in-phase to out-of-phase oscillations or vice versa when the interactions involve a time delay. Here we show that, in the absence of time delay, relay coupling through conjugate variables has the same effect. However, this phase-flip transition does not occur abruptly at a certain critical value of the coupling parameter. Instead we find a parameter region around the phase-flip transition where bistability occurs. In this parameter interval in-phase and out-of-phase oscillations coexist with changing sizes of their basins of attraction. Further increase of the coupling strength leads to amplitude death and subsequently to the stabilization of a fixed point. These transitions are characterized through various quantities such as the average phase difference and crossings in the spectrum of Lyapunov exponents. Numerical results are presented for a specific case of coupled Rössler-like oscillators. © 2011 American Physical Society.

Potential of synthetic genetic network, Repressilator, to work as logical computing unit is observed. It is shown that two variables of gene network yield simultaneously, the basic AND or OR gate with their complementary NAND or NOR gate, with the variation of the internal parameter of the system. This allows the gene network to work as a strong candidate for parallel computing. Stability or robustness of gates is also checked in noisy background. (C) 2012 Elsevier B.V. All rights reserved.

In many bistable oscillating systems only one of the attractors is desired to possessing certain system performance. We present a method to drive a bistable system to a desired target attractor by annihilating the other one. This shift from bistability to monostability is achieved by augmentation of the nonlinear oscillator with a linear control system. For a proper choice of the control function one of the attractors disappears at a critical coupling strength in an control-induced boundary crisis. This transition from bistability to monostability is demonstrated with two paradigmatic examples, the autonomous Chua oscillator and a neuronal system with a periodic input signal. (C) 2013 Elsevier B.V. All rights reserved.

The study of evolving structures and patterns has always been a central point in understanding the universe, ranging from molecular processes at the nanoscale to the galaxies. Recent approaches have adopted machine learning techniques to study these dynamical systems. Here, we implemented the graph neural network to predict the spatiotemporal pattern formation in the ordering of a ferromagnet (nonconserved system) and phase separation of a binary mixture (conserved system). We show that our model can predict the evolution of the nonconserved system with good accuracy. However, prediction for the conserved system fails to preserve the conservation of the order parameter. Furthermore, we find that the prediction for the domain coarsening characterized by a single length scale is consistent with the Allen-Cahn growth law for ferromagnetic ordering. In contrast, we observe deviation from the Lifshitz-Slyozov growth law for the phase-separating binary mixture. Beyond the Ising ferromagnet and binary alloys, our model could be applied to the evolution of other nonequilibrium phenomena, such as surface-directed spinoidal decomposition and percolation. © 2025 Author(s).