Design strategies for the creation of aperiodic nonchaotic attractors

Parametric modulation in nonlinear dynamical systems can give rise to attractors on which the dynamics is aperiodic and nonchaotic, namely with largest Lyapunov exponent being nonpositive. We describe a procedure for creating such attractors by using random modulation or pseudo-random binary sequences with arbitrarily long recurrence times. As a consequence the attractors are geometrically fractal and the motion is aperiodic on experimentally accessible timescales. A practical realization of such attractors is demonstrated in an experiment using electronic circuits.Comment: 9 pages. CHAOS, In Press, (2009

Intermittent large deviation of chaotic trajectory in Ikeda map: Signature of extreme events

We notice signatures of extreme events-like behavior in a laser based Ikeda map. The trajectory of the system occasionally travels a large distance away from the bounded chaotic region, which appears as intermittent spiking events in the temporal dynamics. The large spiking events satisfy the conditions of extreme events as usually observed in dynamical systems. The probability density function of the large spiking events shows a long-tail distribution consistent with the characteristics of rare events. The inter-event intervals obey a Poisson-like distribution. We locate the parameter regions of extreme events in phase diagrams. Furthermore, we study two Ikeda maps to explore how and when extreme events terminates via mutual interaction. A pure diffusion of information exchange is unable to terminate extreme events where synchronous occurrence of extreme events is only possible even for large interaction. On the other hand, a threshold-activated coupling can terminate extreme events above a critical value of mutual interaction.Comment: 11 pages, 9 figure

Synchronization in counter-rotating oscillators

An oscillatory system can have clockwise and anticlockwise senses of rotation. We propose a general rule how to obtain counter-rotating oscillators from the definition of a dynamical system and then investigate synchronization. A type of mixed synchronization emerges in counter-rotating oscillators under diffusive scalar coupling when complete synchronization and antisynchronization coexist in different state variables. Stability conditions of mixed synchronization are obtained analytically in Rossler oscillator and Lorenz system. Experimental evidences of mixed synchronization are given for limit cycle as well as chaotic oscillators in electronic circuits.Comment: 9 pages, 11 figure

Coexisting synchronous and asynchronous states in locally coupled array of oscillators by partial self-feedback control

We report the emergence of coexisting synchronous and asynchronous subpopulations of oscillators in one dimensional arrays of identical oscillators by applying a self-feedback control. When a self-feedback is applied to a subpopulation of the array, similar to chimera states, it splits into two/more sub-subpopulations coexisting in coherent and incoherent states for a range of self-feedback strength. By tuning the coupling between the nearest neighbors and the amount of self-feedback in the perturbed subpopulation, the size of the coherent and the incoherent sub-subpopulations in the array can be controlled, although the exact size of them is unpredictable. We present numerical evidence using the Landau-Stuart (LS) system and the Kuramoto-Sakaguchi (KS) phase model.Comment: 13 pages, 13 figures, accepted for publication in CHAOS (July 2017

Role of membrane environment and membrane-spanning protein regions in assembly and function of the Class II Major Histocompatibility complex

Class II Major Histocompatibility complex (MHC-II) is a polymorphic heterodimer that binds antigen-derived peptides and presents them on the surface of antigen presenting cells. This mechanism of antigen presentation leads to recognition by CD4 T-cells and T-cell activation, making it a critical element of adaptive immune response. For this reason, the structural determinants of MHC-II function have been of great interest for the past 30 years, resulting in a robust structural understanding of the extracellular regions of the complex. However, the membrane-localized regions have also been strongly implicated in protein-protein and protein-lipid interactions that facilitate Class II assembly, transport and function, and it is these regions that are the focus of this review. Here we describe studies that reveal the strong and selective interactions between the transmembrane domains of the MHC α, and invariant chains which, when altered, have broad reaching impacts on antigen presentation and Class II function. We also summarize work that clearly demonstrates the link between membrane lipid composition (particularly the presence of cholesterol) and MHC-II conformation, subsequent peptide binding, and downstream T-cell activation. We have integrated these studies into a comprehensive view of Class II transmembrane domain biology. [Abstract copyright: Copyright © 2018. Published by Elsevier Inc.

Transition from amplitude to oscillation death in a network of oscillators

We report a transition from a homogeneous steady state (HSS) to inhomogeneous steady states (IHSSs) in a network of globally coupled identical oscillators. We perturb a synchronized population in the network with a few local negative mean field links. It is observed that the whole population splits into two clusters for a certain number of negative mean field links and specific range of coupling strength. For further increases of the strength of interaction these clusters collapse to a HSS followed by a transition to IHSSs. We analytically determine the origin of HSS and its transition to IHSS in relation to the number of negative mean-field links and the strength of interaction using a reductionism approach to the model network in a two-cluster state. We verify the results with numerical examples of networks using the paradigmatic Landau-Stuart limit cycle system and the chaotic Rossler oscillator as dynamical nodes. During the transition from HSS to IHSSs, the network follows the Turing type symmetry breaking pitchfork or transcritical bifurcation depending upon the system dynamics.Comment: 6 pages, 5 figures, accepted in Chaos: An Interdisciplinary Journal of Nonlinear Scienc