Showing papers by "Ramakrishna Ramaswamy published in 2012"
TL;DR: This work confirms the enhancing of critical coupling in the chaotic regimes of the Lorenz system, in the Rössler system in the absence of coupling delay, and in the Mackey-Glass system with delay coupling.
Abstract: In a chain of mutually coupled oscillators, the coupling threshold for synchronization between the outermost identical oscillators decreases when a type of impurity (in terms of parameter mismatch) is introduced in the inner oscillator(s). The outer oscillators interact indirectly via dynamic relaying, mediated by the inner oscillator(s). We confirm this enhancing of critical coupling in the chaotic regimes of the Lorenz system, in the Rossler system in the absence of coupling delay, and in the Mackey-Glass system with delay coupling. The enhancing effect is experimentally verified in the electronic circuit of Rossler oscillators.
30 citations
TL;DR: It is found that while the fluctuations of mass have a power spectrum that varies as 1/f for frequencies in the range 3^{-2n}≪f≪1/T, the activity fluctuations in the same frequency range have aPower spectrum that is linear in f.
Abstract: We consider a directed Abelian sandpile on a strip of size $2\ifmmode\times\else\texttimes\fi{}n$, driven by adding a grain randomly at the left boundary after every $T$ timesteps. We establish the exact equivalence of the problem of mass fluctuations in the steady state and the number of zeros in the ternary-base representation of the position of a random walker on a ring of size ${3}^{n}$. We find that while the fluctuations of mass have a power spectrum that varies as $1/f$ for frequencies in the range ${3}^{\ensuremath{-}2n}\ensuremath{\ll}f\ensuremath{\ll}1/T$, the activity fluctuations in the same frequency range have a power spectrum that is linear in $f$.
16 citations
TL;DR: The dynamics observed with finite precision computation shows sensitivity to numerical precision: the minimum accuracy required to obtain "true" trajectories is proportional to an internal timescale that can be defined for the adiabatic system.
Abstract: We study the robustness of dynamical phenomena in adiabatically driven nonlinear mappings with skew-product structure. Deviations from true orbits are observed when computations are performed with inadequate numerical precision for monotone, periodic, or quasiperiodic driving. The effect of slow modulation is to “freeze” orbits in long intervals of purely contracting or purely expanding dynamics in the phase space. When computations are carried out with low precision, numerical errors build up phantom instabilities which ultimately force trajectories to depart from the true motion. Thus, the dynamics observed with finite precision computation shows sensitivity to numerical precision: the minimum accuracy required to obtain “true” trajectories is proportional to an internal timescale that can be defined for the adiabatic system.