arXiv subjects

Sudeshna Sinha

Publications and source records attributed to Sudeshna Sinha.

At least 37 records · Page 2Linked to original sources

arXiv2018

Control of Hierarchical Networks by Coupling to an External Chaotic System

We explore the behaviour of chaotic oscillators in hierarchical networks coupled to an external chaotic system whose intrinsic dynamics is dissimilar to the other oscillators in the network. Specifically, each oscillator couples to the mean-field of the oscillators below it in the hierarchy, and couples diffusively to the oscillator above it in the hierarchy. We find that coupling to one dissimilar external system manages to suppress the chaotic dynamics of all the oscillators in the network at sufficiently high coupling strength. This holds true irrespective of whether the connection to the external system is direct or indirect through oscillators at another level in the hierarchy. Investigating the synchronization properties show that the oscillators have the same steady state at a particular level of hierarchy, whereas the steady state varies across different hierarchical levels. We quantify the efficacy of control by estimating the fraction of random initial states that go to fixed points, a measure analogous to basin stability. These quantitative results indicate the easy controllability of hierarchical networks of chaotic oscillators by an external chaotic system, thereby suggesting a potent method that may help design control strategies.

nlin.CD↗

arXiv2018

Anticipating Persistent Infection

We explore the emergence of persistent infection in a closed region where the disease progression of the individuals is given by the SIRS model, with an individual becoming infected on contact with another infected individual within a given range. We focus on the role of synchronization in the persistence of contagion. Our key result is that higher degree of synchronization, both globally in the population and locally in the neighborhoods, hinders persistence of infection. Importantly, we find that early short-time asynchrony appears to be a consistent precursor to future persistence of infection, and can potentially provide valuable early warnings for sustained contagion in a population patch. Thus transient synchronization can help anticipate the long-term persistence of infection. Further we demonstrate that when the range of influence of an infected individual is wider, one obtains lower persistent infection. This counter-intuitive observation can also be understood through the relation of synchronization to infection burn-out.

nlin.CG↗

arXiv2018

Identifying nodal properties that are crucial for the dynamical robustness of multi-stable networks

We investigate the collective dynamics of bi-stable elements connected in different network topologies, ranging from rings and small-world networks, to scale-free networks and stars. We estimate the dynamical robustness of such networks by introducing a variant of the concept of multi-node basin stability, which allows us to gauge the global stability of the dynamics of the network in response to local perturbations affecting a certain class of nodes of a system. We show that perturbing nodes with high closeness and betweeness-centrality significantly reduces the capacity of the system to return to the desired state. This effect is very pronounced for a star network which has one hub node with significantly different closeness/betweeness-centrality than all the peripheral nodes. In such a network, perturbation of the single hub node has the capacity to destroy the collective state. On the other hand, even when a majority of the peripheral nodes are strongly perturbed, the hub manages to restore the system to its original state, demonstrating the drastic effect of the centrality of the perturbed node on the dynamics of the network. Further, we explore explore Random Scale-Free Networks of bi-stable dynamical elements. We exploit the difference in the distribution of betweeness centralities, closeness centralities and degrees of the nodes in Random Scale-Free Networks with m=1 and m=2, to probe which centrality property most influences the robustness of the collective dynamics in these heterogeneous networks. Significantly, we find clear evidence that the betweeness centrality of the perturbed node is more crucial for dynamical robustness, than closeness centrality or degree of the node. This result is important in deciding which nodes to safeguard in order to maintain the collective state of this network against targeted localized attacks.

nlin.CD↗

arXiv2017

Coexistence of attractors in a coupled nonlinear delayed system modelling El Niño Southern Oscillations

We study the dynamics of the sea surface temperature (SST) anomaly using a model of the temporal patterns of two sub-regions, mimicking behaviour similar to El Niño Southern Oscillations (ENSO). Specifically, we present the existence, stability, and basins of attraction of the solutions arising in the model system in the space of these parameters: self delay, delay and inter-region coupling strengths. The emergence or suppression of oscillations in our models is a dynamical feature of utmost relevance, as it signals the presence or absence of ENSO-like oscillations. In contrast to the well-known low order model of ENSO, where the influence of the neighbouring regions on the region of interest is modelled as external noise, we consider neighbouring regions as a coupled deterministic dynamical systems. Different parameters yield a rich variety of dynamical patterns in our model, ranging from steady states and homogeneous oscillations to irregular oscillations and coexistence of oscillatory attractors, without explicit inclusion of noise. Interestingly, if we take the self-delay coupling strengths of the two sub-regions to be such that the temperature of one region goes to a fixed point regime when uncoupled, while the other system is in the oscillatory regime, then on coupling both systems show oscillations. We explicitly obtain the basins of attraction for the different steady states and oscillatory states in the model. Our results might be helpful for forecasting of El Niño (or La Niña) progress, as it indicates the combination of initial SST anomalies in the sub-regions that can result in a El Niño/La Niña episodes. In particular, the result suggests using an interval as a criterion to estimate the El-Niño or La-Niña progress instead of the currently used the single value criterion.

nlin.CD↗

arXiv2017

Effect of Heterogeneity in Models of El-Niño Southern Oscillations

The emergence of oscillations in models of the El-Niño effect is of utmost relevance. Here we investigate a coupled nonlinear delay differential system modeling theEl-Niño/ Southern Oscillation (ENSO) phenomenon, which arises through the strong coupling of the ocean-atmosphere system. In particular, we study the temporal patterns of the sea surface temperature anomaly of the two sub-regions. For identical sub-regions we typically observe a co-existence of amplitude and oscillator death behavior for low delays, and heterogeneous oscillations for high delays, when inter-region coupling is weak. For moderate inter-region coupling strengths one obtains homogeneous oscillations for sufficiently large delays and amplitude death for small delays. When the inter-region coupling strength is large, oscillations are suppressed altogether, implying that strongly coupled sub-regions do not exhibit ENSO-like oscillations. Further we observe that larger strengths of self-delay coupling favours oscillations, while oscillations die out when the delayed coupling is weak. This indicates again that delayed feedback, incorporating oceanic wave transit effects, is the principal cause of oscillatory behaviour. So the effect of trapped ocean waves propagating in a basin with closed boundaries is crucial for the emergence of ENSO. Further, we show how non-uniformity in delays, and difference in the strengths of the self-delay coupling of the sub-regions, affect the rise of oscillations. Interestingly we find that larger delays and self-delay coupling strengths lead to oscillations, while strong inter-region coupling kills oscillatory behaviour. Thus, we find that coupling sub-regions has a very significant effect on the emergence of oscillations, and strong coupling typically suppresses oscillations, while weak coupling of non-identical sub-regions can induce oscillations, thereby favouring ENSO.

physics.ao-ph↗

arXiv2017

Threshold-activated transport stabilizes chaotic populations to steady states

We explore Random Scale-Free networks of populations, modelled by chaotic Ricker maps, connected by transport that is triggered when population density in a patch is in excess of a critical threshold level. Our central result is that threshold-activated dispersal leads to stable fixed populations, for a wide range of threshold levels. Further, suppression of chaos is facilitated when the threshold-activated migration is more rapid than the intrinsic population dynamics of a patch. Additionally, networks with large number of nodes open to the environment, readily yield stable steady states. Lastly we demonstrate that in networks with very few open nodes, the degree and betweeness centrality of the node open to the environment has a pronounced influence on control. All qualitative trends are corroborated by quantitative measures, reflecting the efficiency of control, and the width of the steady state window.

nlin.CD↗

arXiv2017

Suppression and Revival of Oscillations through Time-varying Interaction

We explore the dynamical consequences of switching the coupling form in a system of coupled oscillators. We consider two types of switching, one where the coupling function changes periodically and one where it changes probabilistically. We find, through bifurcation diagrams and Basin Stability analysis, that there exists a window in coupling strength where the oscillations get suppressed. Beyond this window, the oscillations are revived again. A similar trend emerges with respect to the relative predominance of the coupling forms, with the largest window of fixed point dynamics arising where there is balance in the probability of occurrence of the coupling forms. Further, significantly, more rapid switching of coupling forms yields large regions of oscillation suppression. Lastly, we propose an effective model for the dynamics arising from switched coupling forms and demonstrate how this model captures the basic features observed in numerical simulations and also offers an accurate estimate of the fixed point region through linear stability analysis.

nlin.CD↗

arXiv2016

Multi-node basin stability in complex dynamical networks

Dynamical entities interacting with each other on complex networks often exhibit multistability. The stability of a desired steady regime (e.g., a synchronized state) to large perturbations is critical in the operation of many real-world networked dynamical systems such as ecosystems, power grids, the human brain, etc. This necessitates the development of appropriate quantifiers of stability of multiple stable states of such systems. Motivated by the concept of basin stability (BS) (Menck et al., Nature Physics 9, 89 (2013)), we propose here the general framework of \emph{multi-node basin stability} for gauging global stability and robustness of networked dynamical systems in response to non-local perturbations simultaneously affecting multiple nodes of a system. The framework of multi-node BS provides an estimate of the critical number of nodes which when simultaneously perturbed, significantly reduces the capacity of the system to return to the desired stable state. Further, this methodology can be applied to estimate the minimum number of nodes of the network to be controlled or safeguarded from external perturbations to ensure proper operation of the system. Multi-node BS can also be utilized for probing the influence of spatially localised perturbations or targeted attacks to specific parts of a network. We demonstrate the potential of multi-node BS in assessing the stability of the synchronized state in a deterministic scale-free network of Rössler oscillators and a conceptual model of the power grid of the United Kingdom with second-order Kuramoto-type nodal dynamics.

nlin.CD↗

arXiv2016

Suppression of chaos through coupling to an external chaotic system

We explore the behaviour of an ensemble of chaotic oscillators coupled only to an external chaotic system, whose intrinsic dynamics may be similar or dissimilar to the group. Counter-intuitively, we find that a dissimilar external system manages to suppress the intrinsic chaos of the oscillators to fixed point dynamics, at sufficiently high coupling strengths. So, while synchronization is induced readily by coupling to an identical external system, control to fixed states is achieved only if the external system is dissimilar. We quantify the efficacy of control by estimating the fraction of random initial states that go to fixed points, a measure analogous to basin stability. Lastly, we indicate the generality of this phenomenon by demonstrating suppression of chaotic oscillations by coupling to a common hyper-chaotic system. These results then indicate the easy controllability of chaotic oscillators by an external chaotic system, thereby suggesting a potent method that may help design control strategies.

nlin.CD↗

arXiv2016

Emergence of Persistent Infection due to Heterogeneity

We explore the emergence of persistent infection in a patch of population, where the disease progression of the individuals is given by the SIRS model and an individual becomes infected on contact with another infected individual. We investigate the persistence of contagion qualitatively and quantitatively, under varying degrees of heterogeneity in the initial population. We observe that when the initial population is uniform, consisting of individuals at the same stage of disease progression, infection arising from a contagious seed does not persist. However when the initial population consists of randomly distributed refractory and susceptible individuals, a single source of infection can lead to sustained infection in the population, as heterogeneity facilitates the de-synchronization of the phases in the disease cycle of the individuals. We also show how the average size of the window of persistence of infection depends on the degree of heterogeneity in the initial composition of the population. In particular, we show that the infection eventually dies out when the entire initial population is susceptible, while even a few susceptibles among an heterogeneous refractory population gives rise to a large persistent infected set.

q-bio.PE↗

arXiv2015

Chimera states in Star Networks

We consider star networks of chaotic oscillators, with all end-nodes connected only to the central hub node, under diffusive coupling, conjugate coupling and mean-field type coupling. We observe the existence of chimeras in the end-nodes, which are identical in terms of the coupling environment and dynamical equations. Namely, the symmetry of the end-nodes is broken and co-existing groups with different synchronization features and attractor geometries emerge. Surprisingly, such chimera states are very wide-spread in this network topology, and large parameter regimes of moderate coupling strengths evolve to chimera states from generic random initial conditions. Further, we verify the robustness of these chimera states in analog circuit experiments. Thus it is evident that star networks provide a promising class of coupled systems, in natural or human-engineered contexts, where chimeras are prevalent.

nlin.CD↗

arXiv2015

Balance of interactions determines optimal survival in multi-species communities

We consider a multi-species community modelled as a complex network of populations, where the links are given by a random asymmetric matrix J, with fraction 1-C of zero entries, where C reflects the over-all connectivity of the system. The non-zero elements of J are drawn from a gaussian distribution with mean 'mu' and standard deviation . The signs of the elements J reflect the nature of density-dependent interactions, such as predatory-prey, mutualism or competition, and their magnitudes reflect the strength of the interaction. In this study we try to uncover the broad features of the interspecies interactions that determine the global robustness of this network, as indicated by the average number of active nodes (i.e. non-extinct species) in the network, and the total population, reflecting the biomass yield. We find that the network transitions from a completely extinct system to one where all nodes are active, as the mean interaction strength goes from negative to positive. We also find that the total population, displays distinct non-monotonic scaling behaviour with respect to the product 'mu'C, implying that survival is dependent not merely on the number of links, but rather on the combination of the sparseness of the connectivity matrix and the net interaction strength. Moreover, the total population levels are optimal when the network has intermediate net positive connection strengths. At the local level we observe marked qualitative changes in dynamical patterns, ranging from anti-phase clusters of period 2 cycles and chaotic bands, to fixed points, under the variation of mean 'mu' of the interaction strengths. Lastly, we propose an effective low dimensional map to capture the behavior of the entire network, and this provides a broad understanding of the interplay of the local dynamical patterns and the global robustness trends in the network.

physics.bio-ph↗

arXiv2014

Coupling Reduces Noise

We demonstrate how coupling nonlinear dynamical systems can reduce the effects of noise. For simplicity we investigate noisy coupled map lattices. Noise from different lattice nodes can diffuse across the lattice and lower the noise level of individual nodes. We develop a theoretical model that explains this observed noise evolution and show how the coupled dynamics can naturally function as an averaging filter. Our numerical simulations are in excellent agreement with the model predictions.

nlin.CD↗

arXiv2014

Spatiotemporal Regularity in Networks with Stochastically Varying Links

In this work we investigate time varying networks with complex dynamics at the nodes. We consider two scenarios of network change in an interval of time: first, we have the case where each link can change with probability pt, i.e. the network changes occur locally and independently at each node. Secondly we consider the case where the entire connectivity matrix changes with probability pt, i.e. the change is global. We show that network changes, occurring both locally and globally, yield an enhanced range of synchronization. When the connections are changed slowly (i.e. pt is low) the nodes display nearly synchronized intervals interrupted by intermittent unsynchronized chaotic bursts. However when the connections are switched quickly (i.e. pt is large), the intermittent behavior quickly settles down to a steady synchronized state. Furthermore we find that the mean time taken to reach synchronization from generic random initial states is significantly reduced when the underlying links change more rapidly. We also analyze the probabilistic dynamics of the system with changing connectivity and the stable synchronized range thus obtained is in broad agreement with those observed numerically.

nlin.AO↗

arXiv2013

Taming Explosive Growth through Dynamic Random Links

We study the dynamics of a collection of nonlinearly coupled limit cycle oscillators, relevant to systems ranging from neuronal populations to electrical circuits, under coupling topologies varying from a regular ring to a random network. We find that the trajectories of this system escape to infinity under regular coupling, for sufficiently strong coupling strengths. However, when some fraction of the regular connections are dynamically randomized, the unbounded growth is suppressed and the system always remains bounded. Further we determine the critical fraction of random links necessary for successful prevention of explosive behaviour, for different network rewiring time-scales. These results suggest a mechanism by which blow-ups may be controlled in extended oscillator systems.

nlin.CD↗

arXiv2013

Realization of Morphing Logic Gates in a Repressilator with Quorum Sensing Feedback

We demonstrate how a genetic ring oscillator network with quorum sensing feedback can operate as a robust logic gate. Specifically we show how a range of logic functions, namely AND/NAND, OR/NOR and XOR/XNOR, can be realized by the system, thus yielding a versatile unit that can morph between different logic operations. We further demonstrate the capacity of this system to yield complementary logic operations in parallel. Our results then indicate the computing potential of this biological system, and may lead to bio-inspired computing devices.

physics.bio-ph↗

arXiv2013

Noise-aided Logic in an Electronic Analog of Synthetic Genetic Networks

We report the experimental verification of noise-enhanced logic behaviour in an electronic analog of a synthetic genetic network, composed of two repressors and two constitutive promoters. We observe good agreement between circuit measurements and numerical prediction, with the circuit allowing for robust logic operations in an optimal window of noise. Namely, the input-output characteristics of a logic gate is reproduced faithfully under moderate noise, which is a manifestation of the phenomenon known as Logical Stochastic Resonance. The two dynamical variables in the system yield complementary logic behaviour simultaneously. The system is easily morphed from AND/NAND to OR/NOR logic.

physics.bio-ph↗

arXiv2012

Scalable ultra-sensitive detection of heterogeneity via coupled bistable dynamics

We demonstrate how the collective response of $N$ globally coupled bistable elements can strongly reflect the presence of very few non-identical elements in a large array of otherwise identical elements. Counter-intuitively, when there are a small number of elements with natural stable state different from the bulk of the elements, {\em all} the elements of the system evolve to the stable state of the minority due to strong coupling. The critical fraction of distinct elements needed to produce this swing shows a sharp transition with increasing $N$, scaling as $1/\sqrt{N}$. Furthermore, one can find a global bias that allows robust {\em one bit} sensitivity to heterogeneity. Importantly, the time needed to reach the attracting state does not increase with the system size. We indicate the relevance of this ultra-sensitive generic phenomenon for massively parallelized search applications.

nlin.AO↗