arXiv subjects

Ajay Deep Kachhvah

Publications and source records attributed to Ajay Deep Kachhvah.

17 recordsLinked to original sources

arXiv2022

First-order route to antiphase clustering in adaptive simplicial complexes

This Letter investigates the transition to synchronization of oscillator ensembles encoded by simplicial complexes in which pairwise and higher-order coupling weights alter with time through a rate-based adaptive mechanism inspired by the Hebbian learning rule. These simultaneously evolving disparate adaptive coupling weights lead to a phenomenon in which the in-phase synchronization is completely obliterated; instead, the anti-phase synchronization is originated. In addition, the onsets of antiphase synchronization and desynchronization are manageable through both dyadic and triadic learning rates. The theoretical validation of these numerical assessments is delineated thoroughly by employing Ott-Antonsen dimensionality reduction. The framework and results of the Letter could help in the understanding of the underlying synchronization behavior of a range of real-world systems, such as brain functions and social systems where interactions evolve with time.

cond-mat.dis-nn↗

arXiv2022

Hebbian plasticity rules abrupt desynchronization in pure simplicial complexes

This Letter investigates the upshots of adaptive development of pure 2- and 3- simplicial complexes (triad and tetrad) on the nature of the transition to desynchrony of the oscillator ensembles. The adaptation exercised in the pure simplicial coupling takes a cue from the Hebbian learning rule, i.e., the coupling weight of a triad (tetrad) is prone to increase if the oscillators forming it are in phase and decrease if they are out of phase. The coupling weights in these pure simplicial complexes experiencing such adaptation give rise to first-order routes to desynchronization, whose onsets are entirely characterized by respective Hebbian learning parameters. Mean-field analyses presented for the order parameters for the adaptive 2- and 3- simplicial complexes strongly corroborate with the respective numerical assessments.

nlin.AO↗

arXiv2022

Explosive synchronization and chimera in interpinned multilayer networks

This Letter investigates the nature of synchronization in multilayered and multiplexed populations in which the interlayer interactions are randomly pinned. First, we show that a multilayer network constructed by setting up all-to-all interlayer connections between the two populations leads to explosive synchronization in the two populations successively, leading to the coexistence of coherent and incoherent populations forming chimera states. Second, a multiplex formation of the two populations in which only the mirror nodes are interconnected espouses explosive transitions in the two populations concurrently. The occurrence of both explosive synchronization and chimera are substantiated with rigorous theoretical mean-field analysis. The random pinning in the interlayer interactions concerns the practical problems where the impact of dynamics of one network on that of other interconnected networks remains elusive, as is the case for many real-world systems.

nlin.AO↗

arXiv2021

Machine Learning assisted Chimera and Solitary states in Networks

Chimera and Solitary states have captivated scientists and engineers due to their peculiar dynamical states corresponding to the co-existence of coherent and incoherent dynamical evolution in coupled units in various natural and artificial systems. It has been further demonstrated that such states can be engineered in systems of coupled oscillators by the suitable implementation of communication delays. Here, using supervised machine learning, we predict (a) the precise value of delay which is sufficient for engineering chimera and solitary states for a given set of system parameters, as well as (b) the intensity of incoherence for such engineered states. The results are demonstrated for two different examples consisting of single layer and multi layer networks. First, the chimera states (solitary states) are engineered by establishing delays in the neighboring links of a node (the interlayer links) in a 2-D lattice (multiplex network) of oscillators. Then, different machine learning classifiers, KNN, SVM and MLP-Neural Network are employed by feeding the data obtained from the network models. Once a machine learning model is trained using a limited amount of data, it makes predictions for a given unknown systems parameter values. Testing accuracy, sensitivity, and specificity analysis reveal that MLP-NN classifier is better suited than Knn or SVM classifier for the predictions of parameters values for engineered chimera and solitary states. The technique provides an easy methodology to predict critical delay values as well as the intensity of incoherence for designing an experimental setup to create solitary and chimera states.

nlin.AO↗

arXiv2020

Interlayer Hebbian Plasticity Induces First-Order Transition in Multiplex Networks

Adaptation plays a pivotal role in the evolution of natural and artificial complex systems, and in the determination of their functionality. Here, we investigate the impact of adaptive inter-layer processes on intra-layer synchronization in multiplex networks. The considered adaptation mechanism is governed by a Hebbian learning rule, i.e., the link weight between a pair of interconnected nodes is enhanced if the two nodes are in phase. Such adaptive coupling induces an irreversible first-order transition route to synchronization accompanied with a hysteresis. We provide rigorous analytic predictions of the critical coupling strengths for the onset of synchronization and de-synchronization, and verify all our theoretical predictions by means of extensive numerical simulations.

nlin.AO↗

arXiv2020

Explosive Synchronization in Multilayer Dynamically Dissimilar Networks

The phenomenon of explosive synchronization, which originates from hypersensitivity to small perturbation caused by some form of frustration prevailed in various physical and biological systems, has been shown to lead events of cascading failure of the power grid to chronic pain or epileptic seizure in the brain. Furthermore, networks provide a powerful model to understand and predict the properties of a diverse range of real-world complex systems. Recently, a multilayer network has been realized as a better suited framework for the representation of complex systems having multiple types of interactions among the same set of constituents. This article shows that by tuning the properties of one layer (network) of a multilayer network, one can regulate the dynamical behavior of another layer (network). By taking an example of a multiplex network comprising two different types of networked Kuramoto oscillators representing two different layers, this article attempts to provide a glimpse of opportunities and emerging phenomena multiplexing can induce which is otherwise not possible for a network in isolation. Here we consider explosive synchronization to demonstrate the potential of multilayer networks framework. To the end, we discuss several possible extensions of the model considered here by incorporating real-world properties.

nlin.AO↗

arXiv2019

Inter-layer adaptation induced explosive synchronization in multiplex networks

It is known that intra-layer adaptive coupling among connected oscillators instigates explosive synchronization (ES) in multilayer networks. Taking an altogether different cue in the present work, we consider inter-layer adaptive coupling in a multiplex network of phase oscillators and show that the scheme gives rise to ES with an associated hysteresis irrespective of the network architecture of individual layers. The hysteresis is shaped by the inter-layer coupling strength and the frequency mismatch between the mirror nodes. We provide rigorous mean-field analytical treatment for the measure of global coherence and manifest they are in a good match with respective numerical assessments. Moreover, the analytical predictions provide a complete insight into how adaptive multiplexing suppresses the formation of a giant cluster, eventually giving birth to ES. The study will help in spotlighting the role of multiplexing in the emergence of ES in real-world systems represented by multilayer architecture. Particularly, it is relevant to those systems which have limitations towards change in intra-layer coupling strength.

nlin.AO↗

arXiv2019

Delay engineered solitary states in complex networks

We present a technique to engineer solitary states by means of delayed links in a network of neural oscillators and in coupled chaotic maps. Solitary states are intriguing partial synchronization patterns, where a synchronized cluster coexists with solitary nodes displaced from this cluster and distributed randomly over the network. We induce solitary states in the originally synchronized network of identical nodes by introducing delays in the links for a certain number of selected network elements. It is shown that the extent of displacement and the position of solitary elements can be completely controlled by the choice (values) and positions (locations) of the incorporated delays, reshaping the delay engineered solitary states in the network.

nlin.AO↗

arXiv2019

Taming Chimeras in Networks through Multiplexing Delays

Chimera referring to a coexistence of coherent and incoherent states, is traditionally very difficult to control due to its peculiar nature. Here, we provide a recipe to construct chimera states in the multiplex networks with the aid of multiplexing-delays. The chimera state in multiplex networks is produced by introducing heterogeneous delays in a fraction of inter-layer links, referred as multiplexing-delay, in a sequence. Additionally, the emergence of the incoherence in the chimera state can be regulated by making appropriate choice of both inter- and intra-layer coupling strengths, whereas the extent and the position of the incoherence regime can be regulated by appropriate placing and {strength} of the multiplexing delays. The proposed technique to construct such {engineered} chimera equips us with multiplex network's structural parameters as tools in gaining both qualitative- and quantitative-control over the incoherent section of the chimera states and, in turn, the chimera. Our investigation can be of worth in controlling dynamics of multi-level delayed systems and attain desired chimeric patterns.

nlin.AO↗

arXiv2019

Inhibition induced explosive synchronization in multiplex networks

To date, explosive synchronization (ES) is shown to be originated from either degree-frequency correlation or inertia of phase oscillators. Of late, it has been shown that ES can be induced in a network by adaptively controlled phase oscillators. Here we show that ES is a generic phenomenon and can occur in any network by appropriately multiplexing it with another layer. We devise an approach which leads to the occurrence of ES with hysteresis loop in a network upon its multiplexing with a negatively coupled (or inhibitory) layer. We discuss the impact of various structural properties of positively coupled (or excitatory) and inhibitory layer along with the strength of multiplexing in gaining control over the induced ES transition. This investigation is a step forward in highlighting the importance of multiplex framework not only in bringing novel phenomena which are not possible in an isolated network but also in providing more structural control over the induced phenomena.

nlin.AO↗

arXiv2018

Delay Regulated Explosive Synchronization in Multiplex Networks

It is known that explosive synchronization (ES) in an isolated network of Kuramoto oscillators with inertia is significantly enhanced by the presence of time delay. Here we show that time delay in one layer of the multiplex network governs the transition to synchronization and ES in the other layers. We found that a single layer with time-delayed intra-layer coupling, depending on the values of time delay, experiences a different type of transition to synchronization, e.g., ES or continuous, and the same type of transition is incorporated simultaneously in other layer(s) as well. Hence, a suitable choice of time-delay in only one layer can lead to a desired (either ES or continuous) transition simultaneously in the delayed and other undelayed layers of multiplexed network. These results offer a platform for a better understanding of the dynamics of those complex systems which are represented by multilayered framework and contain time delays in the communication processes.

nlin.AO↗

arXiv2017

Multiplexing induced explosive synchronization in Kuramoto oscillators with inertia

Explosive synchronization (ES) of coupled oscillators on networks is shown to be originated from existence of correlation between natural frequencies of oscillators and degrees of corresponding nodes. Here, we demonstrate that ES is a generic feature of multiplex network of second-order Kuramoto oscillators and can exist in absence of a frequency-degree correlation. A monoplex network of second-order Kuramoto oscillators bearing homogeneous (heterogeneous) degree-distribution is known to display the first-order (second-order) transition to synchronization. We report that multiplexing of two such networks having homogeneous degree-distribution support the first-order transition in both the layers thereby facilitating ES. More interesting is the multiplexing of a layer bearing heterogeneous degree-distribution with another layer bearing homogeneous degree-distribution, which induces a first-order (ES) transition in the heterogeneous layer which was incapable of showing the same in the isolation. Further, we report that such induced ES transition in the heterogeneous layer of multiplex networks can be controlled by varying inter and intra-layer coupling strengths. Our findings emphasize on importance of multiplexing or impact of one layer on dynamical evolution of other layers of systems having inherent multiplex or multilevel architecture.

physics.soc-ph↗

arXiv2016

The effect of distributed time-delays on the synchronization of neuronal networks

Here we investigate the synchronization of networks of FitzHugh-Nagumo neurons coupled in scale-free, small-world and random topologies, in the presence of distributed time delays in the coupling of neurons. We explore how the synchronization transition is affected when the time delays in the interactions between pairs of interacting neurons are non-uniform. We find that the presence of distributed time-delays does not change the behavior of the synchronization transition significantly, vis-a-vis networks with constant time-delay, where the value of the constant time-delay is the mean of the distributed delays. We also notice that a normal distribution of delays gives rise to a transition at marginally lower coupling strengths, vis-a-vis uniformly distributed delays. These trends hold across classes of networks and for varying standard deviations of the delay distribution, indicating the generality of these results. So we conclude that distributed delays, which may be typically expected in real-world situations, do not have a notable effect on synchronization. This allows results obtained with constant delays to remain relevant even in the case of randomly distributed delays.

physics.comp-ph↗

arXiv2014

Transmission of packets on a hierarchical network: Statistics and explosive percolation

We analyze an idealized model for the transmission or flow of particles, or discrete packets of information, in a weight bearing branching hierarchical 2-D networks, and its variants. The capacities add hierarchically down the clusters. Each node can accommodate a limited number of packets, depending on its capacity and the packets hop from node to node, following the links between the nodes. The statistical properties of this system are given by the Maxwell - Boltzmann distribution. We obtain analytical expressions for the mean occupation numbers as functions of capacity, for different network topologies. The analytical results are shown to be in agreement with the numerical simulations. The traffic flow in these models can be represented by the site percolation problem. It is seen that the percolation transitions in the 2-D model and in its variant lattices are continuous transitions, whereas the transition is found to be explosive (discontinuous) for the V- lattice, the critical case of the 2-D lattice. We discuss the implications of our analysis.

cond-mat.stat-mech↗

arXiv2014

Time delay enhanced synchronization in a star network of second order Kuramoto oscillators

We examine the onset of synchronization transition in a star network of Kuramoto phase oscillators in the presence of inertia and a time delay in the coupling. A direct correlation between the natural frequencies of the oscillators and their degrees is assumed. The presence of time delay is seen to enhance the onset of first order synchronization. The star network also exhibits different synchronization transitions depending on the value of time delay. An analytical prediction to observe the effect of the time delay is provided and further supported by simulation results. Our findings may help provide valuable insights into the understanding of mechanisms that lead to synchronization on complex networks.

nlin.AO↗

arXiv2014

Transmission of packets on a hierarchical network: Avalanches, statistics and explosive percolation

We discuss transport on load bearing branching hierarchical networks which can model diverse systems which can serve as models of river networks, computer networks, respiratory networks and granular media. We study avalanche transmissions and directed percolation on these networks, and on the V lattice, i.e., the strongest realization of the lattice. We find that typical realizations of the lattice show multimodal distributions for the avalanche transmissions, and a second order transition for directed percolation. On the other hand, the V lattice shows power - law behavior for avalanche transmissions, and a first order (explosive) transition to percolation. The V lattice is thus the critical case of hierarchical networks. We note that small perturbations to the V lattice destroy the power-law behavior of the distributions, and the first order nature of the percolation. We discuss the implications of our results.

cs.SI↗

arXiv2011

Avalanche transmission and critical behavior in load bearing hierarchical networks

The strength and stability properties of hierarchical load bearing networks and their strengthened variants have been discussed in recent work. Here, we study the avalanche time distributions on these load bearing networks. The avalanche time distributions of the V- lattice, a unique realization of the networks, show power-law behavior when tested with certain fractions of its trunk weights. All other avalanche distributions show Gaussian peaked behavior. Thus the V- lattice is the critical case of the network. We discuss the implications of this result.

cond-mat.stat-mech↗