Ram Ramaswamy

Amplitude Death: The emergence of stationarity in coupled nonlinear systems

When nonlinear dynamical systems are coupled, depending on the intrinsic dynamics and the manner in which the coupling is organized, a host of novel phenomena can arise. In this context, an important emergent phenomenon is the complete suppression of oscillations, formally termed amplitude death (AD). Oscillations of the entire system cease as a consequence of the interaction, leading to stationary behavior. The fixed points which the coupling stabilizes can be the otherwise unstable fixed points of the uncoupled system or can correspond to novel stationary points. Such behavior is of relevance in areas ranging from laser physics to the dynamics of biological systems. In this review we discuss the characteristics of the different coupling strategies and scenarios that lead to AD in a variety of different situations, and draw attention to several open issues and challenging problems for further study.

Identification of insertion hot spots for non-LTR retrotransposons: computational and biochemical application to Entamoeba histolytica

The genome of the human pathogen Entamoeba histolytica contains non-long terminal repeat (LTR) retrotransposons, the EhLINEs and EhSINEs, which lack targeted insertion. We investigated the importance of local DNA structure, and sequence preference of the element-encoded endonuclease (EN) in selecting target sites for retrotransposon insertion. Pre-insertion loci were tested computationally to detect unique features based on DNA structure, thermodynamic considerations and protein interaction measures. Target sites could readily be distinguished from other genomic sites based on these criteria. The contribution of the EhLINE1-encoded EN in target site selection was investigated biochemically. The sequence-specificity of the EN was tested in vitro with a variety of mutated substrates. It was possible to assign a consensus sequence, 5′-GCATT-3′, which was efficiently nicked between A-T and T-T. The upstream G residue enhanced EN activity, possibly serving to limit retrotransposition in the A+T-rich E.histolytica genome. Mutated substrates with poor EN activity showed structural differences compared with normal substrates. Analysis of retrotransposon insertion sites from a variety of organisms showed that, in general, regions of favorable DNA structure were recognized for retrotransposition. A combination of favorable DNA structure and preferred EN nicking sequence in the vicinity of this structure may determine the genomic hotspots for retrotransposition.

Local Properties of Vigilance States: EMD Analysis of EEG Signals during Sleep-Waking States of Freely Moving Rats

Understanding the inherent dynamics of the EEG associated to sleep-waking can provide insights into its basic neural regulation. By characterizing the local properties of the EEG using power spectrum, empirical mode decomposition (EMD) and Hilbert-spectral analysis, we can examine the dynamics over a range of time-scales. We analyzed rat EEG during wake, NREMS and REMS using these methods. The average instantaneous phase, power spectral density (PSD) of intrinsic mode functions (IMFs) and the energy content in various frequency bands show characteristic changes in each of the vigilance states. The 2nd and 7th IMFs show changes in PSD for wake and REMS, suggesting that those modes may carry wake- and REMS-associated cognitive, conscious and behavior-specific information of an individual even though the EEG may appear similar. The energy content in θ2 (6Hz-9Hz) band of the 1st IMF for REMS is larger than that of wake. The decrease in the phase function of IMFs from wake to REMS to NREMS indicates decrease of the mean frequency in these states, respectively. The rate of information processing in waking state is more in the time scale described by the first three IMFs than in REMS state. However, for IMF5-IMF7, the rate is more for REMS than that for wake. We obtained Hilbert-Huang spectral entropy, which is a suitable measure of information processing in each of these state-specific EEG. It is possible to evaluate the complex dynamics of the EEG in each of the vigilance states by applying measures based on EMD and Hilbert-transform. Our results suggest that the EMD based nonlinear measures of the EEG can provide useful estimates of the information possessed by various oscillations associated with the vigilance states. Further, the EMD-based spectral measures may have implications in understanding anatamo-physiological correlates of sleep-waking behavior and clinical diagnosis of sleep-pathology.

Driving-induced multistability in coupled chaotic oscillators: Symmetries and riddled basins

We study the multistability that results when a chaotic response system that has an invariant symmetry is driven by another chaotic oscillator. We observe that there is a transition from a desynchronized state to a situation of multistability. In the case considered, there are three coexisting attractors, two of which are synchronized and one is desynchronized. For large coupling, the asynchronous attractor disappears, leaving the system bistable. We study the basins of attraction of the system in the regime of multistability. The three attractor basins are interwoven in a complex manner, with extensive riddling within a sizeable region of (but not the entire) phase space. A quantitative characterization of the riddling behavior is made via the so-called uncertainty exponent, as well as by evaluating the scaling behavior of tongue-like structures emanating from the synchronization manifold.

Amplitude death: the cessation of oscillations in coupled nonlinear dynamical systems

Here we extend a recent review (Physics Reports 521, 205 (2012)) of amplitude death, namely the suppression of oscillations due to the coupling interactions between nonlinear dynamical systems. This is an important emergent phenomenon that is operative under a variety of scenarios. We summarize results of recent studies that have significantly added to our understanding of the mechanisms that underlie the process, and also discuss the phase–flip transition, a characteristic and unusual effect that occurs in the transient dynamics as the oscillations die out.

Driving-induced bistability in coupled chaotic attractors.

We examine the effects of symmetry-preserving and -breaking interactions in a drive-response system where the response has an invariant symmetry in the absence of the drive. Subsequent to the onset of generalized synchronization, we find that there can be more than one stable attractor. Numerical as well as analytical results establish the presence of phase synchrony in such coexisting attractors. These results are robust to external noise.

Stochastic synchronization of circadian rhythms

Models of circadian genetic oscillators involving interlinked feedback processes in molecular level genetic networks in Drosophila melanogaster and Neurospora crassa are studied, and mechanisms whereby synchronization can arise in an assembly of cells are examined. The individual subcellular circadian oscillatory processes are stochastic in nature due to the small numbers of molecules that are involved, and are subject to large fluctuations. The authors investigate and present the simulations of the stochastic dynamics of ensembles of clock-regulating proteins in different nuclei that communicate via ancillary small molecules, environmental parameters, additive cellular noise, or through diffusive processes. The results show that the emergence of collective oscillations is a macroscopic observable which has its origins in the microscopic coupling between distinct cellular oscillators.

Coupled Lorenz oscillators near the Hopf boundary: Multistability, intermingled basins, and quasiriddling

We investigate the dynamics of coupled identical chaotic Lorenz oscillators just above the subcritical Hopf bifurcation. In the absence of coupling, the motion is on a strange chaotic attractor and the fixed points of the system are all unstable. With the coupling, the unstable fixed points are converted into chaotic attractors, and the system can exhibit a multiplicity of coexisting attractors. Depending on the strength of the coupling, the motion of the individual oscillators can be synchronized (both in and out of phase) or desynchronized and in addition there can be mixed phases. We find that the basins have a complex structure: the state that is asymptotically reached shows extreme sensitivity to initial conditions. The basins of attraction of these different states are characterized using a variety of measures and depending on the strength of the coupling, they are intermingled or quasiriddled.

Amplitude death phenomena in delay-coupled Hamiltonian systems.

Hamiltonian systems, when coupled via time-delayed interactions, do not remain conservative. In the uncoupled system, the motion can typically be periodic, quasiperiodic, or chaotic. This changes drastically when delay coupling is introduced since now attractors can be created in the phase space. In particular, for sufficiently strong coupling there can be amplitude death (AD), namely, the stabilization of point attractors and the cessation of oscillatory motion. The approach to the state of AD or oscillation death is also accompanied by a phase flip in the transient dynamics. A discussion and analysis of the phenomenology is made through an application to the specific cases of harmonic as well as anharmonic coupled oscillators, in particular the Hénon-Heiles system.

Stochastic synchronization of interacting pathways in testosterone model

We examine the possibilities of various coupling mechanisms among a group of identical stochastic oscillators via Chemical Langevin formalism where each oscillator is modeled by stochastic model of testosterone (T) releasing pathway. Our results show that the rate of synchrony among the coupled oscillators depends on various parameters namely fluctuating factor, coupling constants [symbol; see text], and interestingly on system size. The results show that synchronization is achieved much faster in classical deterministic system rather than stochastic system. Then we do large scale simulation of such coupled pathways using stochastic simulation algorithm and the detection of synchrony is measured by various order parameters such as synchronization manifolds, phase plots etc and found that the proper synchrony of the oscillators is maintained in different coupling mechanisms and support our theoretical claims. We also found that the coupling constant follows power law behavior with the systems size (V) by [symbol; see text] ~ AV(-γ), where γ=1 and A is a constant. We also examine the phase transition like behavior in all coupling mechanisms that we have considered for simulation. The behavior of the system is also investigated at thermodynamic limit; where V → ∞, molecular population, N → ∞ but N/V → finite, to see the role of noise in information processing and found the destructive role in the rate of synchronization.