Emergent order in adaptively rewired networks.

We explore adaptive link change strategies that can lead a system to network configurations that yield ordered dynamical states. We propose two adaptive strategies based on feedback from the global synchronization error. In the first strategy, the connectivity matrix changes if the instantaneous synchronization error is larger than a prescribed threshold.

Robustness of the emergence of synchronized clusters in branching hierarchical systems under parametric noise.

The dynamical robustness of networks in the presence of noise is of utmost fundamental and applied interest. In this work, we explore the effect of parametric noise on the emergence of synchronized clusters in diffusively coupled Chaté-Manneville maps on a branching hierarchical structure. We consider both quenched and dynamically varying parametric noise.

Impact of coupling on neuronal extreme events: Mitigation and enhancement.

We focus on the emergence of extreme events in a collection of aperiodic neuronal maps, under local diffusive coupling, as well as global mean-field coupling. Our central finding is that local diffusive coupling enhances the probability of occurrence of both temporal and spatial extreme events, while in marked contrast, global mean-field coupling suppresses extreme events. So the nature of the coupling crucially determines whether the extreme events are enhanced or mitigated by coupling.

Neuronal diversity can improve machine learning for physics and beyond.

Diversity conveys advantages in nature, yet homogeneous neurons typically comprise the layers of artificial neural networks. Here we construct neural networks from neurons that learn their own activation functions, quickly diversify, and subsequently outperform their homogeneous counterparts on image classification and nonlinear regression tasks. Sub-networks instantiate the neurons, which meta-learn especially efficient sets of nonlinear responses.

Influence of the Allee effect on extreme events in coupled three-species systems.

We considered the dynamics of two coupled three-species population patches by incorporating the Allee effect and focused on the onset of extreme events in the coupled system. First, we showed that the interplay between coupling and the Allee effect may change the nature of the dynamics, with regular periodic dynamics becoming chaotic in a range of Allee parameters and coupling strengths. Further, the growth in the vegetation population displays an explosive blow-up beyond a critical value of the coupling strength and Allee parameter.

Machine-learning potential of a single pendulum.

Reservoir computing offers a great computational framework where a physical system can directly be used as computational substrate. Typically a "reservoir" is comprised of a large number of dynamical systems, and is consequently high dimensional. In this work, we use just a single simple low-dimensional dynamical system, namely, a driven pendulum, as a potential reservoir to implement reservoir computing.

Quenching of oscillations in a liquid metal via attenuated coupling.

In this work, we report a quenching of oscillations observed upon coupling two chemomechanical oscillators. Each one of these oscillators consists of a drop of liquid metal submerged in an oxidizing solution. These pseudoidentical oscillators have been shown to exhibit both periodic and aperiodic oscillatory behavior.

Emergent noise-aided logic through synchronization.

In this article, we present a dynamical scheme to obtain a reconfigurable noise-aided logic gate that yields all six fundamental two-input logic operations, including the xor operation. The setup consists of two coupled bistable subsystems that are each driven by one subthreshold logic input signal, in the presence of a noise floor. The synchronization state of their outputs robustly maps to two-input logic operations of the driving signals, in an optimal window of noise and coupling strengths.

Ill-matched timescales in coupled systems can induce oscillation suppression.

We explore the behavior of two coupled oscillators, considering combinations of similar and dissimilar oscillators, with their intrinsic dynamics ranging from periodic to chaotic. We first investigate the coupling of two different real-world systems, namely, the chemical mercury beating heart oscillator and the electronic Chua oscillator, with the disparity in the timescales of the constituent oscillators. Here, we are considering a physical situation that is not commonly addressed: the coupling of sub-systems whose characteristic timescales are very different.

Enhancement of extreme events through the Allee effect and its mitigation through noise in a three species system.

We consider the dynamics of a three-species system incorporating the Allee Effect, focussing on its influence on the emergence of extreme events in the system. First we find that under Allee effect the regular periodic dynamics changes to chaotic. Further, we find that the system exhibits unbounded growth in the vegetation population after a critical value of the Allee parameter.

Competitive interplay of repulsive coupling and cross-correlated noises in bistable systems.

The influence of noise on synchronization has potential impact on physical, chemical, biological, and engineered systems. Research on systems subject to common noise has demonstrated that noise can aid synchronization, as common noise imparts correlations on the sub-systems. In our work, we revisit this idea for a system of bistable dynamical systems, under repulsive coupling, driven by noises with varying degrees of cross correlation.

Construction of logic gates exploiting resonance phenomena in nonlinear systems.

A two-state system driven by two inputs has been found to consistently produce a response mirroring a logic function of the two inputs, in an optimal window of moderate noise. This phenomenon is called logical stochastic resonance (LSR). We extend the conventional LSR paradigm to implement higher-level logic architecture or typical digital electronic structures via carefully crafted coupling schemes.

Asymmetry induced suppression of chaos.

We explore the dynamics of a group of unconnected chaotic relaxation oscillators realized by mercury beating heart systems, coupled to a markedly different common external chaotic system realized by an electronic circuit. Counter-intuitively, we find that this single dissimilar chaotic oscillator manages to effectively steer the group of oscillators on to steady states, when the coupling is sufficiently strong. We further verify this unusual observation in numerical simulations of model relaxation oscillator systems mimicking this interaction through coupled differential equations.

Physics-enhanced neural networks learn order and chaos.

Artificial neural networks are universal function approximators. They can forecast dynamics, but they may need impractically many neurons to do so, especially if the dynamics is chaotic. We use neural networks that incorporate Hamiltonian dynamics to efficiently learn phase space orbits even as nonlinear systems transition from order to chaos.

Advent of extreme events in predator populations.

We study the dynamics of a ring of patches with vegetation-prey-predator populations, coupled through interactions of the Lotka-Volterra type. We find that the system yields aperiodic, recurrent and rare explosive bursts of predator density in a few isolated spatial patches from time to time. Further, the global predator biomass also exhibits sudden uncorrelated occurrences of large deviations from the mean as the coupled system evolves.

Echo in complex networks.

Large populations of globally coupled or uncoupled oscillators have been recently shown to exhibit an intriguing echo behavior [Ott, Platig, Antonsen, and Girvan, Chaos: An Interdiscip. J. Nonlinear Sci.

Localized spatial distributions of disease phases yield long-term persistence of infection.

We explore the emergence of persistent infection in two patches where the phases of disease progression of the individuals is given by the well known SIRS cycle modelling non-fatal communicable diseases. We find that a population structured into two patches with significantly different initial states, yields persistent infection, though interestingly, the infection does not persist in a homogeneous population having the same average initial composition as the average of the initial states of the two patches. This holds true for inter-patch links ranging from a single connection to connections across the entire inter-patch boundary.

The knowledge level of rheumatoid arthritis patients about their disease in a developing country. A study in 168 Bangladeshi RA patients.

Objectives: To assess disease-related knowledge of rheumatoid arthritis (RA) patients PATIENTS AND METHODS: Consecutive RA patients were invited from the rheumatology departments of BSMM University, Dhaka, Bangladesh. The Bangla version of the Patient Knowledge Questionnaire (B-PKQ) was used. Correlations between the B-PKQ scores and clinical-demographic data were measured using Pearson's correlation coefficient.

Explosive death in nonlinear oscillators coupled by quorum sensing.

Many biological and chemical systems exhibit collective behavior in response to the change in their population density. These elements or cells communicate with each other via dynamical agents or signaling molecules. In this work, we explore the dynamics of nonlinear oscillators, specifically Stuart-Landau oscillators and Rayleigh oscillators, interacting globally through dynamical agents in the surrounding environment modeled as a quorum sensing interaction.

Emergence of extreme events in networks of parametrically coupled chaotic populations.

We consider a collection of populations modelled by the prototypical chaotic Ricker map, relevant to the population growth of species with non-overlapping generations. The growth parameter of each population patch is influenced by the local mean field of its neighbourhood, and we explore the emergent patterns in such a parametrically coupled network. In particular, we examine the dynamics and distribution of the local populations, as well as the total biomass.

Chaotic attractor hopping yields logic operations.

Certain nonlinear systems can switch between dynamical attractors occupying different regions of phase space, under variation of parameters or initial states. In this work we exploit this feature to obtain reliable logic operations. With logic output 0/1 mapped to dynamical attractors bounded in distinct regions of phase space, and logic inputs encoded by a very small bias parameter, we explicitly demonstrate that the system hops consistently in response to an external input stream, operating effectively as a reliable logic gate.

Identifying nodal properties that are crucial for the dynamical robustness of multistable networks.

We investigate the collective dynamics of bistable elements connected in different network topologies and estimate the network response to localized perturbations on different classes of nodes by introducing a variant of the concept of multinode basin stability. We show that perturbations on nodes with high closeness and betweeness centrality drastically reduces the capacity of the system to return to the original state. This effect is most pronounced for a star network, where perturbation of the single hub node can destroy the collective state, while the system manages to recover even when a majority of the peripheral nodes are strongly perturbed.

Emergence of synchronization and regularity in firing patterns in time-varying neural hypernetworks.

We study synchronization of dynamical systems coupled in time-varying network architectures, composed of two or more network topologies, corresponding to different interaction schemes. As a representative example of this class of time-varying hypernetworks, we consider coupled Hindmarsh-Rose neurons, involving two distinct types of networks, mimicking interactions that occur through the electrical gap junctions and the chemical synapses. Specifically, we consider the connections corresponding to the electrical gap junctions to form a small-world network, while the chemical synaptic interactions form a unidirectional random network.

Time-varying multiplex network: Intralayer and interlayer synchronization.

A large class of engineered and natural systems, ranging from transportation networks to neuronal networks, are best represented by multiplex network architectures, namely a network composed of two or more different layers where the mutual interaction in each layer may differ from other layers. Here we consider a multiplex network where the intralayer coupling interactions are switched stochastically with a characteristic frequency. We explore the intralayer and interlayer synchronization of such a time-varying multiplex network.

Small-world networks exhibit pronounced intermittent synchronization.

We report the phenomenon of temporally intermittently synchronized and desynchronized dynamics in Watts-Strogatz networks of chaotic Rössler oscillators. We consider topologies for which the master stability function (MSF) predicts stable synchronized behaviour, as the rewiring probability (p) is tuned from 0 to 1. MSF essentially utilizes the largest non-zero Lyapunov exponent transversal to the synchronization manifold in making stability considerations, thereby ignoring the other Lyapunov exponents.